Calculus Learning Outcomes

Students will determine expressions and values using mathematical procedures and rules, translate mathematical information from a single representation or across multiple representations, justify reasoning and solutions; and use correct notation, language, and mathematical conventions to communicate results or solutions in the following areas of study.

1.1 Velocity and Distance

1.2 Calculus without Limits

1.3 Velocity and Distance

1.4 Circular Motion

1.5 Circular Motion

2.1 The Derivative of a Function

2.2 Powers and Polynomials

2.3 The Slope and the Tangent Line

2.4 Derivative of the Sine and Cosine

2.5 The Product and Quotient and Power Rules

2.6 Limits

2.7 Continuous Functions

3.1 Linear Approximation

3.2 Maximum and Minimum Problems

3.3 Second Derivatives: Minimum vs. Maximum

3.4 Graphs

3.5 Ellipses, Parabolas, and Hyperbolas

3.6 Iterations x[n+1] = F(x[n])

3.7 Newton’s Method and Chaos

3.8 The Mean Value Theorem and l’Hopital’s Rule

4.1 Derivatives by the Chain Rule

4.2 Implicit Differentiation and Related Rates

4.3 Inverse Functions and Their Derivatives

4.4 Inverses of Trigonometric Functions

5.1 The Idea of an Integral

5.2 Antiderivatives

5.3 Summation vs. Integration

5.4 Indefinite Integrals and Substitutions

5.5 The Definite Integral

5.6 Properties of the Integral and the Average Value

5.7 The Fundamental Theorem and Its Consequences

5.8 Numerical Integration

6.1 An Overview

6.2 The Exponential e^x

6.3 The Exponential e^x

6.4 Logarithms

6.5 Separable Equations Including the Logistic Equation

6.6 Powers Instead of Exponentials

6.7 Hyperbolic Functions

7.1 Integration by Parts

7.2 Trigonometric Integrals

7.3 Trigonometric Substitutions

7.4 Partial Fractions

7.5 Improper Integrals

8.1 Areas and Volumes by Slices

8.2 Length of a Plane Curve

8.3 Area of a Surface of Revolution

8.4 Probability and Calculus

8.5 Masses and Moments

8.6 Force, Work, and Energy

9.1 Polar Coordinates

9.2 Polar Equations and Graphs

9.3 Slope, Length, and Area for Polar Curves

9.4 Complex Numbers

10.1 The Geometric Series

10.2 Convergence Tests: Positive Series

10.3 Convergence Tests: All Series

10.4 The Taylor Series for e^x, sin x, and cos x