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Course Descriptions
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All Whatcom Community College math courses are 5 credits with the following exceptions.
 MATH 207 Taylor Series (1 credit)
 MATH 208  Sequences and Series (3 credits)
Expand/Contract Questions and Answers
(coordinator: Lee Singleton)
Textbook: Algebra: A Combined Course, by Charles P. McKeague
Course Description:
The first in a two course elementary algebra sequence. The course will include solving one variable linear equations, formulas and applications, polynomial operations, factoring, and an introduction to solving nonlinear equations with quadratic formula or by using inverse operations. Graphing calculators are required.Prerequisite: MATH 94 or equivalent with a grade of "S" or better.
Course Outcomes: Students will be able to…
1.
Solve linear equations and inequalities of one variable.
2.
Solve nonlinear equations with one variable by using inverse operations.
3.
Solve application problems involving linear equations.
4.
Add, subtract, multiply, and divide polynomial expressions.
5.
Factor polynomials.
6.
Solve quadratic equations.
Course Content:
 Numerical Operations and Expressions
Optional: Review of Fractions, Operations, Order of Operations [0.2, 0.6 or Ch. 0 Rev.]
Absolute Value, Variables, Perimeter, Area [1.1]
Properties of Real Numbers (includes inverse operations, distributing) [1.5]
Simplifying Expressions (Terms, Like Terms) [1.6]
 Solving Linear Equations
Addition Property of Equality [2.1]
Multiplication Property of Equality [2.2]
Solve Linear Equations in One Variable [2.3]
 Words in Problems and Inequalities
Intro to Formulas (plug known values and evaluate for remaining) [2.4, first part]
Applications (number, age, perimeter, coin) [2.5]
Applications (Integer, interest, triangle, misc) [2.6]
Linear Inequalities [2.7]
 Inverse Operations: Roots and Powers
Roots of Real Numbers (includes square and cube roots) [S.1]
Solve Simple NonLinear Equations (includes 2^{nd} and 3^{rd} powers and roots) [S.2]
 Polynomials
Exponent Rules: Multiplication with Exponents, Sci. Notation [5.1]
Polynomial Operations: Addition, Subtraction [5.4]
Polynomial Operations: Multiplication, Special Products [5.5, 5.6]
Exponent Rules: Division with Exponents (no negative exponents) [S.3]
Polynomial Operations: Division by Monomial, Binomial [5.7, 5.8]
 Factoring
Factoring (GCF, Grouping) [6.1]
Factoring Quadratics (a=1, a not equal to 1) [6.2, 6.3]
Special Factoring (difference of squares, perfect square trinomials) [6.4]
General Factoring Review [6.6]
Solve Equations by Factoring [6.7]
Factoring Applicatons [6.8]
 Solve NonFactorable Quadratics (No complex solutions)
*Note: Could include S.1 and S.2 here instead
Quadratic Formula Introduction [S.4]
 Numerical Operations and Expressions
(coordinator: Yumi Watanabe)
Textbook: Algebra: A Combined Course, by Charles P. McKeague
Course Description:
Second in a two course elementary algebra sequence. Students are expected to be proficient in the first half of an Elementary Algebra course sequence (Math 97 or equivalent). Topics include dimensional analysis, graphing, exponent rules, systems of equations, radical equations, quadratic equations, and applications of elementary algebra. Graphing Calculators are required.Prerequisite: MATH 97 or equivalent with a grade of "C" or better.
Course Outcomes: Students will be able to…
1.
Graph and interpret linear equations.
2.
Use a variety of methods to solve systems of linear equations. (includes substitution, elimination, and graphical methods)
3.
Simplify expressions using exponent rules.
4.
Simplify radical expressions.
5.
Solve radical equations.
6.
Solve quadratic equations with real or complex solutions.
7.
Solve application problems involving linear, quadratic, and radical equations.
Course Content:
 Ratios/Proportions [S.1]
 Dimensional Analysis [S.2]
 Graphing
 Graphing Coordinates [3.1]
 Solutions and Graphs of Lines, Graphs with Intercepts [3.2, 3.3]
 Slope, Graphing with Slope [3.4]
 Finding equations of given lines [3.5]
 Graph Linear Inequalities (twovariable) [3.6]
 Systems of Equations (2x2)
 Graphing [4.1]
 Substitution [4.2]
 Elimination [4.3]
 Applications [4.4]
 Exponent Rules
 Multiplication, Division, Simplifying [(Review 5.1), 5.2, 5.3]
 Radicals
(Note: Extensive coverage of higher roots throughout all sections)
 Rational Exponents [10.1]
 Simplify Expressions [10.2, 10.3, 10.4]
 Solve Equations (Square Roots and Higher Roots) [10.5 part 1]
 Basic Graph Exposure (Square Root and Higher Roots) [10.5 part 2]
 Complex Numbers [10.6]
 Quadratics
 Solving Quadratics (Factor, Complete Square, Q.F.– complex possible) [11.1, 11.2]
 Finding Equations with Given Solutions [11.3]
 Solve with Quadratic Forms [11.4]
 Graphs of Quadratics [11.5]
 Solve Quadratic Inequalities [11.6 (first part)]
 Ratios/Proportions [S.1]
(coordinator: Jeannette Stephens)
Textbook: Algebra: A Combined Course, by Charles P. McKeague
Course Description:
A course in functions and fundamentals of algebra intended to prepare students planning to take additional courses in science, technology, engineering, and mathematics. Topics include rational expressions and equations, functions and graphs, systems of equations (3variable and nonlinear), exponential and logarithmic functions, and right triangle trigonometry. Graphing calculator required.Prerequisite: MATH 98 or equivalent with a grade of "C" or better.
Course outcomes: Students will be able to…
1.
Simplify rational expressions and solve rational equations.
2.
Determine the domain and range of a function represented either graphically, numerically or symbolically.
3.
Evaluate functions and their sums, differences, products, quotients, and compositions.
4.
Analyze the effects of parameter changes on the graphs of functions.
5.
Graph and solve simple exponential and logarithmic equations.
6.
Solve systems of equations with up to 3 variables (includes linear and nonlinear systems using graphing, substitution, elimination, and calculator methods).
7.
Apply the basic trigonometric relationships to right triangles.
Course Content:
 Rational Functions/Expressions
 Simplify Expressions [7.1]
 Multiply/Divide Rational Expressions [7.2]
 Add/Subtract Rational Expressions [7.3]
 Solve Equations [7.4]
 Applications [7.5]
 Complex Fractions [7.6]
 Variation [7.8]
 Functions
 Intro to Functions, Function Notation [8.6, 8.7]
 Function Algebra (includes composition) [8.8]
 Basic Function Graphs (Line, quadratic, abs. value, cube, square root) [S.1]
 Transformations (vertical and horizontal stretch and shifts, reflections) [S.2]
 Inverse Functions (could include here or with Exp. and Log section) [12.2]
 Exponential & Log Intro
 Exponential Functions and Applications [12.1]
*Could include inverses here, see function section* [12.2]
 Log Functions, Graphs, Applications [12.3]
*can intro change of base early if graphing with calculator*
 Common and Natural Log, (solve simple logs) [12.5]
 Change of Base, solve simple Exponential equations, applications [12.6]
*Limit solving to same base equations or just changing exp>log or log>exp (like pH equation)*
 Systems of Equations
 Systems Review (Graph, Sub, Elim.) [9.1]
 Larger Linear Systems [9.2]
 Larger Linear Systems (Calculator Methods – rref) [9.3]
 Applications of Systems [9.5]
 Intro to Nonlinear Systems (2x2) (substitution, or elimination) [13.5 (second part)]

Trig Unit [S.3]
 Rational Functions/Expressions
(coordinator: Jeannette Stephens)
Textbook: Mathematical Ideas, 12th edition by Miller, Heeren, and Hornsby
Course Description:
Exploration of mathematical concepts with emphasis on observing closely, developing critical thinking, analyzing and synthesizing techniques, improving problem solving skills, and applying concepts to new situations. Core topics are probability and statistics. Additional topics may be chosen from a variety of math areas useful in our society. Graphing calculator required.Prerequisite: MATH 99 or equivalent with a grade of "C" or better.
Course outcomes: Students will be able to…
1.
Compute experimental and theoretical probabilities including: odds, complements, compound, conditional, and expected value.
2.
Analyze and summarize data displayed in tabular and graphical form.
3.
Compute measures of central tendency, measures of dispersion, measures of position, and areas under the Standard Normal Curve.
4.
Compute the regression line for bivariate linear data.
5.
Solve application problems using growth/decay models including: linear, exponential, and logarithmic models.
6.
Compute future and present value, simple and compound interest, credit card debt, annuities, and financial loans.
7.
Interpret, analyze, and summarize models and sets of data using appropriate mathematical terminology.
Course Content:
 Probability [Ch. 11]
 Statistics [Ch. 12]
 Exponential and Logarithmic Functions, Applications, and Models [Sec. 8.6]
 Personal Finance Management [Ch. 13]
Time permitting additional topics can be chosen from topics at the discretion of the instructor. Some examples are listed below.
 The Basic Concepts of Set Theory (as an introduction to probability) [Ch. 2]
 Counting Methods (permutations and combinations, etc.) [Ch. 10]
 Voting and Apportionment [Ch. 16]
 Probability [Ch. 11]
(coordinator: Crystal Holtzheimer)
Textbook: Quantitative Reasoning and the Environment: Mathematical Modeling in Context, 1st edition by Langkamp and Hull
Course Description:
Exploration of linear, power, exponential, logistic, logarithmic, and difference equations using data analysis. Students will create mathematical models from environmentally themed data sets to better understand different types of relationships between variables. Quantitative reasoning will be heavily emphasized. A graphing calculator is required.Prerequisite: MATH 99 or equivalent with a grade of "C" or better.
Course outcomes: Students will be able to…
1. Create mathematical models for environmental data sets. These include linear, exponential, power, difference equation, and logistic models.
2. Determine the most appropriate model to use for a specific set of data.
3. Use mathematical models to analyze the behavior of environmental data.
4. Solve linear, exponential, power, and difference equations.
Course Content:
 Linear Functions and Regression [Ch. 4]
 Modeling with Linear Functions
 Units of Measure in Linear Equations
 Dependent versus Independent Variables
 Graphing Linear Functions
 Approximating AlmostLinear Data Sets
 The straightedge method
 Least Squares Regression
 The Correlation Coefficient
 Correlation Fallacies
 Exponential Functions and Regression [Ch. 5]
 Exponential Rates and Multipliers
 The General Exponential Model
 Finding Exponential FunctionsThe More General Case
 Solving Exponential Equations
 Doubling Times and HalfLives
 Approximating AlmostExponential Data Sets
 Power Functions [Ch. 6]
 Basic Power Functions
 Solving Power Equations
 Approximating PowerLike Data
 Power Law Distributions and Fractals
 Introduction to Difference Equations [Ch. 7]
 Sequences and Notation
 Modeling with Difference Equations
 Linear Difference Equations
 Exponential Difference Equations
 Why Use Difference Equations?
 Affine Difference Equations
 Affine Solution Equations and Equilibrium Values [Ch. 8]
 The Solution Equation to the Affine Model
 Equilibrium Values
 Classification of Equilibrium Values
 Logistic Growth, harvesting and Chaos [Ch. 9]
 Modeling Logistic Growth with Difference Equations
 Logistic Equilibrium Values
 Harvest Models
 Periodic Behavior
 Chaotic Behavior
 Optional
 Systems of Difference Equationsa
 Exponential Change and Stable Age Distributions
 Linear Functions and Regression [Ch. 4]
(coordinator: Nathan Hall)
Textbook: Precalculus: Mathematics for Calculus, 7th Edition by Stewart, Redlin, and Watson
Course Description:
The basic properties and graphs of functions and inverses of functions, operations on functions, compositions; various specific functions and their properties including polynomial, absolute value, rational, exponential and logarithmic functions; applications of various functions; conics. A graphing calculator is required.Prerequisite: MATH 99 or equivalent with a grade of "C" or better.
Course outcomes: Students will be able to…
1.
Analyze the graphs of polynomial, rational, exponential, logarithmic, and piecewise functions.
2.
Analyze relationships between real and complex zeros, linear factors, and xintercepts of a polynomial function.
3.
Solve polynomial, exponential, and logarithmic equations.
4.
Perform function composition.
5.
Analyze the relationships between graphs of conic sections and their standard equations.
Course Content:
 Complex numbers and operations (should be review) [1.6]
 Polynomials
 Polynomial models to motivate topic (suggested, not required) [3.1]
 Graphs of Polynomials (End behavior, turns, zeros) [3.2]
 Finding zeros of Polynomials (real and complex) [3.3, 3.4] (dividing polynomials and real zeros)
 Theorems: Fundamental Theorem of Algebra, Complex Zeros Theorem [3.5]
 Rational Graphs
 Vertical Asymptotes, Horizontal Asymptotes, Holes, Zeros [3.6]
 Oblique Asymptotes [3.6]
 Piecewise Functions
 Graphing Piecewise Functions [S.1]
 Absolute Value as a Piecewise Function (include piecewise supplement) [S.1]
*topics appear in 2.2, but use Supplement 1 for content and exercises*
 Function Composition
 Algebra of Compositions [2.7]
 Graphing Compositions [2.7]
 Inverse functions [2.8]
 Exponentials and Logs
 Graphs of Exponentials and Logs [4.1, 4.2, 4.3]
 Properties of Logs [4.4]
 Change of base [4.4]
 Solve Exponential and Logarithmic Equations [4.5]
 Applications/Models of Exponentials and Logs [4.6]
 Logarithmic Scales [4.7]
 Conics
 Circles [1.9]
 Parabolas [11.1]
 Ellipses [11.2]
 Hyperbolas [11.3]
 Shifted Conics [11.4]
 Complex numbers and operations (should be review) [1.6]
(coordinator: Lee Singleton)
Textbook: Precalculus: Mathematics for Calculus, 7th Edition by Stewart, Redlin, and Watson
Course Description:
Second in a two course sequence designed to prepare students for the study of Calculus. Intended for students planning to major in math and/or science. Course to include right triangle trigonometry; trigonometric functions and their graphs; trigonometric identities and formulae; applications of trigonometry; parametric equations; polar coordinates. A graphing calculator is required.Prerequisite: MATH& 141 or equivalent with a grade of "C" or better.
Course outcomes: Students will be able to…
1.
Analyze the relationships between right triangles, circles, and trigonometric functions using radian or degree measurements.
2.
Solve geometric problems using triangle relationships. These include right triangle identities, the Law of Sines, and the Law of Cosines.
3.
Relate trigonometric functions to their corresponding graphs, including vertical and horizontal shifts and stretches.
4.
Transform trigonometric expressions using identities. (These include, but are not limited to: quotient, reciprocal, sum and difference, double angle, even/odd, or Pythagorean relationships.)
5.
Solve trigonometric equations symbolically or in reference to an application.
6.
Examine relationships between polar coordinates, Cartesian coordinates, polar equations, and polar graphs. 7.
Analyze relationships between standard equations, parametric equations, and their graphs.
Course Content:

Trigonometric Functions
 Radian and Degree Measure [6.1]
 Right Triangle Trigonometry [6.2]
 The Unit Circle [5.1]
 Trigonometric Functions of Any Angle [5.2, 6.3]
 Graphs of sine and cosine Functions [5.3]
 Graphs of other Trigonometric Functions [5.4]
 Inverse Trigonometric Functions [5.5, 6.4]
 Applications and Models [5.6]
 Laws of Sines [6.5]
 Law of Cosines [6.6]
(This ordering is based on the previous text, but chapters 5 and 6 can be taught in any order. Another combined approach suggested by the text is: 5.1, 5.2, 6.1, 6.2, 6.3, 5.3, 5.4, 5.5, 5.6, 6.4, 6.5, 6.6. Another option is to teach these two chapters sequentially.)
 Analytic Trigonometry
 Fundamental Trigonometric Identities [7.1]
 Verifying Trigonometric Identities [7.1]
 Sum and Difference Formulas [7.2]
 MultipleAngle Formulas (i.e. double angle and half angle) [7.3]
 ProductSum Formulas (optional) [7.3]
 Solving Trigonometric Equations (single and multiple angle) [7.4, 7.5]
 Parametric and Polar Equations
 Polar Coordinates [8.1]
 Graphs of Polar Equations [8.2], (11.6 optional)
 Parametric Equations [8.4]
 Limits
 Introduction to Limits (optional) [13.1]
 Methods of Evaluating Limits (optional) [13.2]

Trigonometric Functions
(coordinator: Doug Mooers)
Textbook: Mathematics with Applications, 10th edition by Lial, Hungerford, and Holcomb
Course Description:
Applications of linear, quadratic, exponential, and logarithmic equations; functions and graphs; mathematics of finance; solution of linear systems using matrices; linear programming using the simplex method. A graphing calculator is required.Prerequisite: MATH 99 or equivalent with a grade of "C" or better.
Course outcomes: Students will be able to…
1. Construct regression models (linear, quadratic, cubic, or quartic) representing data, and use them to solve application problems, calculate residuals; state a correlation coefficient and defend the quality of fit.
2. Evaluate a linear, quadratic, absolute value, rational, polynomial, exponential, logarithmic, piecewise, or greatest integer function. Determine the domain of at least one of these functions.
3. Solve inequalities involving linear, quadratic, absolute value, or rational functions.
4. Graph linear inequalities in two variables.
5. Solve linear programming problems graphically and apply them to business applications.
6. Set up and solve a system of three equations with three unknowns.
7. Calculate business application function values. These include simple interest and discount, compound interest, a breakeven point, an equilibrium point, an annual percentage yield APY, or amortization values.
8. Employ technology to determine the maximum value of the objective function and state where it occurs as an ordered pair.
Course Content:
 Graphs, Lines, and Inequalities
 Graphs [2.1]
 Equations of a Line (slopeintercept, pointslope, general, vertical, horizontal) [2.2]
 Linear Models (Applications) [2.3]
 Linear Inequalities [2.4]
 Polynomial and Rational Inequalities (using graphing calculator) [2.5]
 Functions
 Functions [3.1]
 Graphs of Functions [3.2]
 Applications of Linear Functions [3.3]
 Quadratic Functions [3.4]
 Application of Quadratic Functions [3.5]
 Polynomial Functions [3.6]
 Rational Functions [3.7]
 Exponential and Logarithmic Functions
 Exponential Functions [4.1]
 Applications of Exponential Functions [4.2]
 Logarithmic Functions (solving log equations) [4.3]
 Logarithmic and Exponential Functions (Applications) [4.4]
 Mathematics of Finance
 Simple Interest and Discount [5.1]
 Compound Interest [5.2]
 Annuities, Future Values, Sinking Funds [5.3]
 Present Value of an Annuity: Amortization [5.4]
 Systems of Linear Equations
 Systems of Two Linear Equations in Two Variables [6.1]
 Larger Systems (The GaussJordan Method) [6.2]

Linear Programming
 Systems of Linear Inequalities [7.1]
 Linear Programming (graphical approach) [7.2]
 Application of Linear Programming [7.3]
 The Simplex Method: Maximization [7.4]
 Application of Maximization [7.5]
 Graphs, Lines, and Inequalities
(coordinator: Crystal Holtzheimer)
Textbook: Understandable Statistics, 11th edition by Brase and Brase
Course Description:
Rigorous introduction to statistical methods and hypothesis testing. Includes descriptive and inferential statistics. Tabular and pictorial methods for describing data; central tendencies; mean; modes; medians; variance; standard deviation; quartiles; regression; normal distribution; confidence intervals; hypothesis testing, one and twotailed tests. Applications to business, social sciences, and sciences. Graphing calculator required.Prerequisite: MATH 99 or equivalent with a grade of "C" or better.
Course outcomes: Students will be able to…
1. Interpret values and draw conclusions from data using appropriate statistical terminology.
2. Organize data using tabular and graphical methods.
3. Summarize data using numerical measures of center and spread that are appropriate for the data set.
4. Compute probabilities. These include theoretical, experimental, compound, conditional, binomial, and normal.
5. Create confidence intervals for means, proportions, and differences between means and proportions.
6. Conduct hypothesis tests for means, proportions, correlation coefficients, slopes of least squares lines, and differences between means and proportions.
7. Compute the least squares regression line for bivariate linear data.
Course Content:
 Getting Started
 What is Statistics? [1.1]
 Random Samples [1.2]
 Introduction to Experimental Design [1.3]
 Organizing Data
 Frequency Distributions, Histograms, and Related Topics [2.1]
 Bar Graphs, Circle Graphs, and TimeSeries Graphs [2.2]
 StemandLeaf Display [2.3]
 Averages and Variation
 Measures of Central Tendency: Mode, Median, and Mean [3.1]
 Measures of Variation [3.2]
 Percentiles and BoxandWhisker Plots [3.3]
 Probability
 What is Probability? [4.1]
 Some Probability Rules, Compound Events [4.2]
 Trees and Counting Techniques [4.3]
 Introduction to Random Variables and Probability Distribution [5.1]
 Binomial Probabilities [5.2]
 Additional Properties of the Binomial Distribution [5.3]
 Normal Distributions
 Graphs of Normal Probability Distributions [6.1]
 Standard Units and Areas Under the Standard Normal Distribution [6.2]
 Areas Under Any Normal Curve [6.3]
 Sampling Distributions [6.4]
 The Central Limit Theorem [6.5]
 Normal Approximation to the Binomial and phat Distribution [6.6]

Hypothesis Testing and Confidence Intervals
 Estimating mu when sigma is Known [7.1]
 Estimating mu when sigma is Unknown [7.2]
 Estimating p in the Binomial Distribution [7.3]
 Estimating the Differences Between Means and Proportions [7.4]
 Introduction to Statistical Tests [8.1]
 Testing the Mean [8.2]
 Testing a Proportion [8.3]
 Tests Involving Paired Differences (Dependent Samples) [8.4]
 Testing Independent Samples [8.5]

Linear Regression
 Scatter Diagrams and Linear Correlation [9.1]
 Linear Regression and the Coefficient of Determination [9.2]
 Inferences for Correlation and Regression [9.3]
 Getting Started
(coordinator: Doug Mooers)
Textbook: Mathematics with Applications, 10th edition by Lial, Hungerford, and Holcomb
Course Description:
Limits, derivatives, marginal analysis, optimization, antiderivatives, and definite integrals. Examples taken from management, life and social sciences. A graphing calculator is required.Prerequisite: MATH& 141 or MATH 145 or equivalent with a grade of "C" or better.
Course outcomes: Students will be able to…
1. Apply limit laws algebraically, graphically, or numerically to evaluate real valued limits and limits involving infinity.
2. Determine the first and second derivative of polynomial, exponential, or logarithmic functions. These include the product, quotient, or composition of these functions.
3. Evaluate functions and their sums, differences, products, quotients, and compositions.
4. Apply the concept of a limit, derivative, or continuity to business, management, natural, or social science.
5. Determine the antiderivative of a function.
6. Using the Fundamental Theorem of Calculus, calculate the value of a definite integral.
7. Apply definite and indefinite integrals to applications involving business, management, natural, or social science.
Course Content:
 Differential Calculus
 Limit Laws [11.1]
 Onesided limits, limits at infinity [11.2]
 Rates of Change; Instantaneous velocity [11.3]
 The Derivative; Slope of Tangent [11.4]
 Derivative Laws; Marginal Analysis [11.5]
 Derivative laws; Product Rule; Quotient Rule [11.6]
 The Chain Rule and Function Composition f(g(x)) [11.7]
 Derivative of exponential e^{x} and logarithmic ln(x) [11.8]
 Continuity and Differentiability [11.9]
 Applications of the Derivative
 Derivatives and increasing/decreasing functions, critical points, max & min, first derivative test [12.1]
 Second Derivative: concavity and inflection. Second Derivative Test [12.2]
 Applications. Average Cost, Elasticity (optional) [12.3]
 Graphing: xint, yint; vert. & horiz. asym; inc & dec; concavity, inflection [12.4]
 Integral Calculus
 Antiderivatives. Integral laws [13.1]
 Substitution Method of Integral [13.2]
 Definite Integral. Net Area between xaxis and f(x) [13.3]
 Fundamental Theorem of Calculus (Definite Integral) [13.4]
 Area Between Curves and other Applications [13.5]
 Table of Integrals (optional) [13.6]
 Differentiable Equations, find the function that makes the equation true. (optional) [13.7]
 Differential Calculus
(coordinator: Johnny Hu)
Textbook: Calculus: Early Transcendentals, 7th edition by James Stewart
Course Description:
A traditional first course in differential calculus intended for math and science majors. Some proofs of derivative laws. Study of functions, limits, continuity, limits at infinity, differentiation of algebraic, exponential, logarithmic, and trigonometric functions and their inverses. Applications. A graphing calculator is required.Prerequisite: MATH& 142 or equivalent with a grade of "C" or better.
Course outcomes: Students will be able to…
1. Compute limits using graphical, tabular, algebraic, and L’Hopital’s Rule methods.
2. Apply the definitions of limit, continuity, and derivative appropriately.
3. Determine derivatives of polynomial, exponential, trigonometric, and logarithmic functions, and combinations thereof.
4. Demonstrate the relationship between the derivative as a slope and as a rate of change (ex: velocity and acceleration).
5. Apply the Chain Rule to differentiate and implicitly differentiate functions.
6. Develop and analyze math models for related rate and optimization problems.
7. Calculate extrema and inflection points using derivative analysis.
8. Analyze the behavior of a function using graphical, tabular, or algebraic representations of the derivative of the function.
9. Apply the Mean Value Theorem.
10. Use Newton’s Methods to approximate the solution of an equation.
Course Content:
 Limits
 Tangent & Velocity [2.1]
 Limit of a Function [2.2]
 Limit Laws, Squeeze Theorem [2.3]
 Delta Epsilon Limits [2.4]
 Continuity [2.5]
 Limits at Infinity [2.6]
 Derivatives: Rates of Change [2.7]
 Derivative of a Function [2.8]
 Derivatives
 Derivatives: Polynomial and Exponential f(x) [3.1]
 Product & Quotient Rules [3.2]
 Trig Function Derivatives [3.3]
 Chain Rule [3.4]
 Implicit Differentiation, Inverse Trig Derivatives [3.5]
 Log Function Derivatives [3.6]
 Rates of Change: Natural/Social Science [3.7]
 Related Rates [3.9]
 Differentials and Linear Approximations [3.10]
 Hyperbolic Functions (focus on derivatives) [3.11]
 Applications of the Derivative
 Maximum and Minimum Values [4.1]
 Mean Value & Rolle's Theorem [4.2]
 Derivatives and Graphing [4.3]
 Indeterminate Form, L'Hospital's Rule [4.4]
 Applications: Optimization [4.7]
 Newton's Method [4.8]
 Limits
(coordinator: Johnny Hu)
Textbook: Calculus: Early Transcendentals, 7th edition by James Stewart
Course Description:
The Study of Riemann Sums, Methods of Integration, Numerical Methods, Fundamental Theorem of Calculus, Areas of Regions, Volumes of Solids, Centroids, Length of Curves, Surface Area. Course includes an Introduction to Differential Equations. A graphing calculator is required.Prerequisite: MATH& 151 or equivalent with a grade of "C" or better.
Course outcomes: Students will be able to…
1. State fundamental antiderivatives and their integral representations.
2. Utilize a Riemann sum in determining a definite integral.
3. Use finite sums to approximate the value of definite integrals.
4. Calculate integrals using substitution, parts, partial fractions, and trigonometric methods.
5. Set up definite integrals to calculate areas, volumes and other applications.
6. Use the Fundamental Theorem of Calculus to evaluate definite integrals.
7. Solve separable differential equations.
Course Content:
 Integrals
 Antiderivatives [4.9]
 Area under a curve, sigma notation [5.1]
 Definite Integral [5.2]
 Fundamental Theorem of Calculus [5.3]
 Indefinite Integrals [5.4]
 Substitution Rule [5.5]
 Applications of Integration
 Area between Curves [6.1]
 Volumes (cross sections, disc method) [6.2]
 Volumes (shell method) [6.3]
 Work [6.4]
 Average Value [6.5]

Techniques of Integration
 Integration by Parts [7.1]
 Powers of Trigonometric Functions [7.2]
 Trigonometric Substitution [7.3]
 Method of Partial Fractions [7.4]
 Integration Strategies [7.5]
 Approximate Integration [7.7]
 Improper Integrals [7.8]

Further Applications of Integration
 Arc Length [8.1]
 Surface Area of Solid of Revolution [8.2]
 Centroids [8.3]

Introduction to Differential Equations
 Ordinary Differential Equations [9.1]
 Separable Equations [9.3]
 Integrals
(coordinator: Yumi Watanabe)
Textbook: Calculus: Early Transcendentals, 7th edition by James Stewart
Course Description:
Multivariate integral and differential calculus. Geometry in R3 and in the plane. The study of vectors, acceleration, curvature; functions of several variables, partial derivatives; directional derivatives and gradiants; extreme values; double and triple integrals; applications.Prerequisite: MATH& 152 or equivalent with a grade of "C" or better.
Course outcomes: Students will be able to…
1. Perform vector arithmetic. These include dot and cross products, in geometric and component form.
2. Use vectors to compute projections, equations of lines, and equations of planes.
3. Using the concepts of derivatives and integrals to vectorvalued functions, compute and describe arclength, curvature, and motion in space.
4. Use partial derivatives and the gradient in a variety of applied problems. These include directional derivatives, optimization, linear approximations, and tangent planes.
5. Apply the many forms of the chain rule for partial derivatives as appropriate.
6. Set up and evaluate double and triple integrals.
Course Content:
 Vectors and the Geometry of Space
 ThreeDimensional Coordinate Systems [12.1]
 Vectors [12.2]
 Dot Product [12.3]
 Cross Product [12.4]
 Equations of Lines and Planes. Distance. [12.5]
 Cylinders & Quadric Surfaces [12.6]
 Vector Functions
 Vector Functions [13.1]
 Derivatives & Integrals of Vector Functions [13.2]
 Arc Length & Curvature [13.3]
 Velocity & Acceleration in Space [13.4]
 Partial Derivatives
 Functions of Several Variables [14.1]
 Limits; Continuity [14.2]
 Partial Derivatives [14.3]
 Tangent Planes; Linear Approximations [14.4]
 Chain Rule [14.5]
 Directional Derivatives; Gradient Vector [14.6]
 Maximum/Minimum Values [14.7]
 Lagrange Multipliers [14.8]

Multiple Integrals
 Double Integrals (Rectangular) [15.1]
 Iterated Integrals [15.2]
 Double Integrals (General Regions) [15.3]
 Applications of Double Integrals [15.5]
 Triple Integrals [15.7]
 Vectors and the Geometry of Space
(coordinator: Will Webber)
Textbook: Elementary Linear Algebra: Applications Edition, 10th edition by Anton and Rorres
Course Description:
Elementary study of the fundamentals of linear algebra. Course to include the study of systems of linear equations, matrices, ndimensional vector space, linear independence, bases, subspaces and dimension. Introduction to determinants and the eigenvalue problem, applications. A graphing calculator is required.Prerequisite: MATH& 151 or equivalent with a grade of "C" or better.
Course outcomes: Students will be able to…
1. Use matrices to solve systems of linear equations.
2. Compute vector arithmetic in Rn, including calculations of the dot and the cross products.
3. Prove whether a given set is or is not a vector space.
4. Prove whether a given subset of a vector space is or is not a subspace.
5. For a given set of vectors determine if it spans the vector space, is linearly independent,
and is a basis for the vector space.6. Describe transformations of R2 and R3 using matrices.
7. Solve eigenvalue and eigenvector problems.
Course Content:
 Systems of Linear Equations and Matrices
 Introduction to Systems of Linear Equations [1.1]
 Gaussian Elimination [1.2]
 Matrices and Matrix Operations [1.3]
 Inverses, Algebraic Properties of Matrices [1.4]
 Elementary Matrices and Finding the Inverse Matrix [1.5]
 More on Linear Systems and Invertible Matrices [1.6]
 Diagonal, Triangular, and Symmetric Matrices [1.7]
 Determinants
 Determinants by Cofactor Expansion [2.1]
 Evaluating Determinants by Row Reduction [2.2]
 Properties of Determinants, Cramer's Rule [2.3]
 Euclidean Vector Spaces
 Vectors in 2, 3, and nspace [3.1]
 Norm, Dot Product, and Distance in Rn [3.2]
 Orthogonality [3.3]
 The Geometry of Linear Systems [3.4]
 Cross Product [3.5]
 General Vector Spaces
 Real Vector Spaces [4.1]
 Subspaces [4.2]
 Linear Independence [4.3]
 Coordinates and Basis [4.4]
 Dimension [4.5]
 Change of Basis [4.6]
 Row Space, Column Space, and Null Space [4.7]
 Rank, Nullity, and the Fundamental Matrix Spaces [4.8]
 Matrix Transformations from Rn to Rm [4.9]
 Properties of Matrix Transformations [4.10]
 Geometry of Matrix Operators on R2 [4.11]
 Eigenvalues and Eigenvectors
 Eigenvalues and Eigenvectors [5.1]
 Systems of Linear Equations and Matrices
(coordinator: Johnny Hu)
Textbook: Taylor Polynomials and Taylor Series for MATH 126 (Handout), University of Washington Math Department
Course Description:
Introduction to the derivation and uses of Taylor Series, intended for math and science majors. The course includes a discussion of error bounds in approximating curves with polynomials, Taylor polynomials, Taylor series expansion, and intervals of convergence.Prerequisite: MATH& 152 or equivalent with a grade of "C" or better.
Course outcomes: Students will be able to…
1. Create a Taylor polynomial of finite length for a given function
2. Determine an error bound for a Taylor polynomial approximation to a curve
3. Create a Taylor Series for a given function
Course Content:
 Tangent Line Approximation and Error Bound
 Quadratic Approximation and Error Bound
 Taylor Polynomials
 Higher Order Approximation and Taylor's Inequality
 Taylor Series
 Operations with Taylor Series
 Interval of Convergence
 Tangent Line Approximation and Error Bound
(coordinator: Johnny Hu)
Textbook: Calculus: Early Transcendentals, 7th edition by James Stewart
Course Description:
A course in the techniques of working with infinite sequences and series. It is intended for math and science majors. The course includes Limits of sequences, series, alternating series, absolute and conditional convergence, power series, Taylor and Maclaurin series, applications.Prerequisite: MATH& 152 or equivalent with a grade of "C" or better.
Course outcomes: Students will be able to…
1. Evaluate the limit of a sequence
2. Evaluate the limit of an infinite series
3. Test the convergence of an infinite series
4. Represent a function as a power series
5. Represent a function as a Taylor series
6. Determine the error bound for a Taylor polynomial approximation to a function
7. Use series in application problems
Course Content:
 Infinite Sequences and Series
 Sequences [11.1]
 Series [11.2]
 The Integral Test [11.3]
 The Comparison Tests [11.4]
 Alternating Series [11.5]
 Absolute Convergence and the Ratio and Root Tests [11.6]
 Strategy for Testing Series [11.7]
 Power Series [11.8]
 Representations of Functions as Power Series [11.9]
 Taylor and Maclaurin Series [11.10]
 Applications of Taylor Polynomials [11.11]
 Infinite Sequences and Series
(coordinator: Will Webber)
Textbook: Elementary Differential Equations, 9th edition by Boyce and DiPrima
Course Description:
Introductory course in differential equations. Topics include first and higher order linear equations, power series solutions, systems of first order equations, numerical methods, LaPlace transforms, applications. A graphing calculator is required.Prerequisite: MATH& 152 or equivalent with a grade of "C" or better.
Course outcomes: Students will be able to…
1. Solve first order differential equations using the techniques of separable, linear, autonomous and exact equations.
2. Use approximation techniques to estimate solutions to differential equations.
3. Solve second order homogeneous and linear differential equations.
4. Use differential equations to solve a variety of application problems.
5. Solve nth order linear differential equation.
6. Use power series to solve differential equations.
7. Apply LaPlace transforms to solve differential equations.
Course Content:
 First Order Differential Equations
 Linear Equations, Integrating Factors [2.1]
 Separable Equations [2.2]
 Modeling with First Order Equations [2.3]
 Linear and Nonlinear Equations [2.4]
 Autonomous Equations [2.5]
 Exact Equations [2.6]
 Euler's Method [2.7]
 The Existence and Uniqueness Theorem [2.8]
 Second Order Linear Equations
 Homogeneous Equations with Constant Coefficients [3.1]
 Solutions of Linear Homogeneous Equations, Wronskian [3.2]
 Complex Roots of the Characteristic Equations [3.3]
 Repeated Roots, Reduction of Order [3.4]
 Nonhomogeneous Equations, Method of Undetermined Coefficients [3.5]
 Variation of Parameters [3.6]
 Mechanical and Electrical Vibrations [3.7]
 Forced Vibrations [3.8]
 Higher Order Linear Equations
 nth order Linear Equations [4.1]
 Homogeneous Equations with Constant Coefficients [4.2]
 Method of Undetermined Coefficients [4.3]
 Series Solutions of Second Order Linear Equations
 Power Series [5.1]
 Series Solutions, part I [5.2]
 Series Solutions, part II [5.3]
 Euler Equations [5.4]
 The Laplace Transform
 Definition of the Laplace Transform [6.1]
 Initial Value Problems [6.2]
 Step Functions [6.3]
 First Order Differential Equations
(coordinator: Will Webber)
Textbook: Calculus: Early Transcendentals, 7th edition by James Stewart
Course Description:
This is the second quarter of multivariable calculus. Topics include multiple integration in different coordinate systems, the gradient, the divergence, and the curl of a vector field. Also covered are line and surface integrals, Green’s Theorem, Stoke’s Theorem and Gauss’ Theorem.Prerequisite: MATH& 163 or equivalent with a grade of "C" or better.
Course outcomes: Students will be able to…
1. Compute integrals of two or three variables in the plane or in space.
2. Compute the change in the volume element when coordinate systems are changed.
3. Describe surfaces parametrically.
4. Describe vector fields and their flows.
5. Apply the fundamental theorem for line integrals and Green's theorem in the plane.
6. Compute flux integrals for parametrized surfaces.
7. Apply the divergence theorem to compute flux integrals.
8. Apply the concept of the curl to a vector field.
9. Apply Stoke's theorem to compute flux integrals (and line integrals).
Course Content:
 Multiple Integrals
 Double Integrals over Rectangles [15.1]
 Iterated Integrals [15.2]
 Double Integrals over General regions [15.3]
 Double Integrals in Polar coordinates [15.4]
 Applications of Double integrals [15.5]
 Triple Integrals [15.6]
 Triple Integrals in Cylindrical Coordinates [15.7]
 Triple Integrals in Spherical Coordinates [15.8]
 Change of Variables in Multiple integrals (the Jacobian) [15.9]
 Vector Calculus
 Vector Fields [16.1]
 Line Integrals [16.2]
 The Fundamental Theorem for Line Integrals [16.3]
 Green’s Theorem [16.4]
 Curl and Divergence [16.5]
 Parametric Surfaces and Their Areas [16.6]
 Surface Integrals [16.7]
 Stokes’ Theorem [16.8]
 The Divergence Theorem [16.9]
 Summary [16.10]
 Multiple Integrals
Textbook: Varies, contact the instructor
Course Description:
Courses offered in conjunction with the Whatcom Community College Honors Program. Open only to Whatcom Community College Honors Program students. Limited enrollment of 10 students.
Prerequisite: Varies by course
Course Content:
Contact instructor for a syllabus for a specific quarter and year in which the course is offered.