Course Details - Mathematics and Statistics - Penn State Altoona

Math 110

Techniques of Calculus, I

4 credits

Blue Book Description: Functions, graphs, derivatives, integrals, techniques of differentiation and integration, exponentials, improper integrals, applications. Students may take only one course for credit from MATH 110, 140, 140A, and 140B.

Pre-requisites: MATH 022 or satisfactory performance on the mathematics proficiency examination (score at least 9 on MATH 110 SOAR score).

Pre-requisite for: Math 111, Math 220

Suggested Textbook:
Brief Calculus: An Applied Approach, 8th Edition, by Larson, published by Houghton Mifflin.
Check with your instructor to make sure this is the textbook used for your section.

Topics:
Chapter 1: Functions, Graphs, and Limits
1.1 The Cartesian Plane and the Distance Formula
1.2 Graphs of Equations
1.3 Lines in the Plane and Slope
1.4 Functions
1.5 Limits
1.6 Continuity

Chapter 2: Differentiation
2.1 The Derivative and the Slope of a Graph
2.2 Some Rules for Differentiation
2.4 The Product and Quotient Rules
2.5 The Chain Rule
2.3 Rates of Change: Velocity and Marginals
2.6 Higher-Order Derivatives
2.7 Implicit Differentiation
2.8 Related Rates

Chapter 3: Applications of the Derivative
3.1 Increasing and Decreasing Functions
3.2 Extrema and First-Derivative Test
3.3 Concavity and the Second-Derivative Test
3.4 Optimization Problems
3.5 Business and Economics Applications
3.6 Asymptotes
3.7 Curve Sketching
3.8 Differentials and Marginal Analysis

Chapter 4: Exponential Growth and Logarithmic Functions
4.1 Exponential Functions
4.2 Derivatives of Exponential Functions
4.3 Logarithmic Functions
4.4 Derivatives of Logarithmic Functions
4.5 Exponential Growth and Decay

Chapter 5: Integration and Its Applications
5.1 Antiderivatives and Indefinite Integrals
5.2 Integtation by Substitution and the the General Power Rule
5.3 Exponential and Logarithmic Integrals
5.4 Area and the Fundamental Theorem of Calculus
5.5 The Area of a Region Bounded by Two Graphs
5.6 The Definite Integral as the Limit of a Sum

Chapter 6: Techniques of Integration
6.1 Integration by Parts and Present Value
6.2 Partial Fractions and Logistic Growth (optional)
6.4 Numerical Integration (optional)
6.5 Improper Integrals (optional)