Mathematics, Statistics & Computer Science
University of Wisconsin-Stout
Jarvis Hall Science Wing 231
Menomonie, WI 54751-0790
COURSE NUMBER/TITLE:
MATH-151 Calculus with Precalculus B
(Previously MATH-151 Integrated Calculus B)
CREDITS:
5
COURSE DESCRIPTION:
Second course in a two-course sequence. Calculus with integrated
precalculus. Properties, identities, and derivatives of exponential,
logarithmic, and trigonometric functions. Affine transformations and
graphing, linear systems of equations, and geometric applications of
trigonometry. Integration and the Fundamental Theorem of Calculus.
Prerequisite: MATH-150 Calculus with Precalculus A
TEXTBOOK:
Calculus I with Integrated Precalculus, 1st Ed., by Taalman (adopted Fall 2013)
COURSE OBJECTIVES:
Upon successful completion of the course the student will be able to:
1. Apply affine transformations to the graph of a function.
2. Relate functions to their inverses.
3. Evaluate expressions involving exponentials and logarithms.
4. Apply mathematics to solve real world problems.
5. Compute derivatives of expressions involving exponential and logarithmic functions.
6. Solve geometric problems using trigonometric functions.
7. Evaluate elementary antiderivatives and integrals.
8. Solve systems of linear equations.
COURSE OUTLINE:
1. Affine Transformations (Objective 1)
a. Horizontal and vertical translations
b. Reflections about the x and y axis
c. Horizontal and vertical scaling
2. Inverse Functions (Objective 2)
a. Graphical interpretation
b. The horizontal line test
c. Computing inverse functions and domain restrictions
3. Exponentials and Logarithms (Objectives 2, 3)
a. Definitions and properties of exponential functions
b. Graphing exponential functions
c. Definitions and properties of logarithmic functions
d. Graphing logarithms
e. Equations involving exponentials and logarithms
4. Applications of Exponentials and Logarithms (Objectives 3, 4)
a. Compound interest
b. Exponential growth
c. Half‐life and radioactive decay
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Exponentials, Logarithms and Calculus (Objective 5)
a. The chain rule
b. Derivatives of inverse functions
c. Derivatives of exponentials and logarithms
d. Logarithmic differentiation
Trigonometry (Objective 6)
a. Right triangle trigonometry
b. Unit circle trigonometry
c. Radian measure
d. Graphing trigonometric functions
e. Angle addition and subtraction formulas
f. Inverse trigonometric functions
g. Equations involving trigonometric functions
h. Law of Sines and Law of Cosines
i. Applications of trigonometry
Trigonometry and Calculus (Objective 6)
a. Limits of trigonometric functions
b. Derivatives of trigonometric functions
c. Related rates
Integral Calculus (Objective 7)
a. Antiderivatives of polynomials
b. Antiderivatives of exponential functions
c. Antiderivatives of trigonometric functions
d. Substitution
e. Definite integrals and Riemann Sums
f. The Fundamental Theorem of Calculus
System of Equations (Objective 8)
a. Linear systems of equations
b. Representing systems of equations as augmented matrices
c. Gaussian elimination
Updated 8/2015
Revised 4/2013
1/2011