Differential and integral calculus: limits; continuity; the derivative and applications; extrema; the definite integral; fundamental theorem of calculus; L'Hopital's rule.

Prerequisite:

None

Course Outline:

Section 1.1 and 1.2: Ways to Represent a Function/Mathematical Models

Section 1.3: New Functions from Old

Section Appendix D: Trigonometry

Section 1.4: Exponential Functions

Section 1.5: Inverse Functions and Logarithms

Sections 2.1 and 2.2: Tangent and Velocity Problems/Limit of a Function

Section 2.3A: Calculating Limits, Part 1

Section 2.3B: Calculating Limits, Part 2

Section 2.4: Precise Definition of a Limit

Section 2.5A: Continuity, Part 1

Section 2.5B: Continuity, Part 2

Section 2.6: Limits at Infinity, Horizontal Asymptotes

Section 2.7: Derivatives and Rates of Change

Section 2.8: The Derivative as a Function

Section 3.1: Derivatives of Polynomials and Exponentials

Section 3.2: Product and Quotient Rules

Section 3.3: Derivatives of Trig Functions

Section 3.4: Chain Rule

Section 3.5: Implicit Differentiation

Section 3.6: Derivatives of Log Functions

Section 3.7: Rates of Change in the Natural and Social Sciences

Section 3.9: Related Rates

Section 4.1: Maximum and Minimum Values

Section 4.2: Mean Value Theorem

Section 4.3: Shape of a Graph

Section 4.4: L'Hospital's Rule

Section 4.5: Curve Sketching

Section 4.7A: Optimization, Part 1

Section 4.7B: Optimization, Part 2

Sections 4.8 and 3.10: Newton's Method/Linear Approximation

Section 4.9: Antiderivatives

Appendix E: Sigma Notation

Section 5.1/5.2A: Areas and Distances/Definition of Definite Integral

Section 5.2B: The Definite Integral

Section 5.3A: The Fundamental Theorem of Calculus, Part 1

Section 5.3B: The Fundamental Theorem of Calculus, Part 2

Section 5.4: Indefinite Integrals and Net Change

Section 5.5: Substitution

Section 1.3: New Functions from Old

Section Appendix D: Trigonometry

Section 1.4: Exponential Functions

Section 1.5: Inverse Functions and Logarithms

Sections 2.1 and 2.2: Tangent and Velocity Problems/Limit of a Function

Section 2.3A: Calculating Limits, Part 1

Section 2.3B: Calculating Limits, Part 2

Section 2.4: Precise Definition of a Limit

Section 2.5A: Continuity, Part 1

Section 2.5B: Continuity, Part 2

Section 2.6: Limits at Infinity, Horizontal Asymptotes

Section 2.7: Derivatives and Rates of Change

Section 2.8: The Derivative as a Function

Section 3.1: Derivatives of Polynomials and Exponentials

Section 3.2: Product and Quotient Rules

Section 3.3: Derivatives of Trig Functions

Section 3.4: Chain Rule

Section 3.5: Implicit Differentiation

Section 3.6: Derivatives of Log Functions

Section 3.7: Rates of Change in the Natural and Social Sciences

Section 3.9: Related Rates

Section 4.1: Maximum and Minimum Values

Section 4.2: Mean Value Theorem

Section 4.3: Shape of a Graph

Section 4.4: L'Hospital's Rule

Section 4.5: Curve Sketching

Section 4.7A: Optimization, Part 1

Section 4.7B: Optimization, Part 2

Sections 4.8 and 3.10: Newton's Method/Linear Approximation

Section 4.9: Antiderivatives

Appendix E: Sigma Notation

Section 5.1/5.2A: Areas and Distances/Definition of Definite Integral

Section 5.2B: The Definite Integral

Section 5.3A: The Fundamental Theorem of Calculus, Part 1

Section 5.3B: The Fundamental Theorem of Calculus, Part 2

Section 5.4: Indefinite Integrals and Net Change

Section 5.5: Substitution

Monday–Friday (except holidays)

8:00 a.m.–5:00 p.m. mountain time

Toll-Free: 1-800-914-8931

Local: 801-422-2868

Fax: 801-422-0102

indstudy@byu.edu

Harman Continuing Education Building

770 E University Pkwy

Provo UT 84602

BYU Independent Study

229 HCEB

770 E University Pkwy

Provo UT 84602