Course Details - Mathematics and Statistics - Penn State Altoona

Math 140

Calculus with Analytic Geometry I

4 credits

Blue Book Description: Functions; limits; analytic geometry; derivatives, differentials, applications; integrals, applications. Students may take only one course for credit from MATH 110, 140, 140A, and 140B.

Pre-requisites: MATH 022, 026; or MATH 040 or 041; or satisfactory performance on the mathematics proficiency examination (score at least 14 on MATH 140 SOAR test.

Pre-requisite for: MATH 141, MATH 220

Suggested Textbook:
Single Variable Calculus: Early Transcendentals, Vol 1, 7th edition, by James Stewart, published by Brookes/Cole Centage Learning.
Check with your instructor to make sure this is the textbook used for your section.

Topics:
ADVICE: For first year students with scores less than 19 on MATH 140 SOAR test, MATH 140A is strongly recommended.

Chapter 2: Limits and Derivatives
2.1 The Tangent and Velocity Problems
2.2 The Limit of a Function
2.3 Calculating Limits Using the Limit Laws
2.4 The Precise Definition of a Limit (optional),
2.5 Continuity
2.6 Limits at Infinity; Horizontal Asymptotes
2.7 Derivatives and Rates of Change
2.8 The Derivative as a Function

Chapter 3: Differentiation Rules
3.1 Derivatives of Polynomials and Exponential Functions
3.2 The Product and Quotient Rules
3.3 Derivatives of Trigonometric Functions
3.4 The Chain Rule
3.5 Implicit Differentiation
3.6 Derivatives of Logarithmic Functions
3.7 Rates of Change in Natural and Social Sciences (optional)
3.8 Exponential Growth and Decay (optional)
3.9 Related Rates

Chapter 4: Applications of Differentiation
4.1 Maximum and Minimum Values
4.2 The Mean Value Theorem
4.3 How Derivatives Affect the Shape of a Graph
4.4 Indeterminate Forms and L'Hospital's Rule
4.5 Summary of Curve Sketching
4.7 Optimization Problems
4.9 Antiderivatives

Chapter 5: Integrals
5.1 Areas and Distance
5.2 The Definite Integral
5.3 The Fundamental Theorem of Calculus
5.4 Indefinite Integrals and the Net Change Theorem
5.5 The Substitution Rule

Chapter 6: Applications of Integration
6.1 Areas between Curve
6.2 Volumes
6.2 Volumes by Cylindrical Shells (optional)
6.4 Work (optional)
6.5 Average Value of a Function (optional)