MAC 2311 — Calculus I — Syllabus
Prerequisites: C (2.0) or better in MAC 1114 and C (2.0) or
better in MAC 1140, or C (2.0) or better in MAC 1147, or SAT Math
score of 650 or better, or ACT Math score of 29 or better, or
College-Level Math CPT score of 90 or better, and knowledge of
trigonometry.
Course Description: The course meets for approximately 55 hours during
a 15-week semester. Successful completion of the course merits 4 semester hours
of credit and provides sufficient background for either MAC 2312 (Calculus II)
or MAC 2282 (Engineering Calculus II). The schedule outlined below allows time
for four midterm exams plus a cumulative final exam, which are the norms for
this course. (Note: A “lecture” is defined as a 50-minute time
period.)
Text: Calculus: Early Transcendental Functions, 4th Edition,
by Larson, Hostetler, and Edwards
Course Content
Chapter 1 Preparation for Calculus (1-2 weeks)
1.1 Graphs and Models
1.2 Linear Models and Rates of Change
1.3 Functions and Their Graphs
1.4 Fitting Models to Data
1.5 Inverse Functions
1.6 Exponential and Logarithmic Functions
Chapter 2 Limits and Their Properties (2-3 weeks)
2.1 A Preview of Calculus
2.2 Finding Limits Graphically and Numerically
2.3 Evaluating Limits Analytically
2.4 Continuity and One-Sided Limits
2.5 Infinite Limits
Chapter 3 Differentiation (3-4 weeks)
3.1 The Derivative and the Tangent Line Problem
3.2 Basic Differentiation Rules and Rates of Change
3.3 Product and Quotient Rules and Higher-Order Derivatives
3.4 The Chain Rule
3.5 Implicit Differentiation
3.6 Derivatives of Inverse Functions
3.7 Related Rates
3.8 Newton's Method (optional)
Chapter 4 Applications of Differentiation (3-4 weeks)
4.1 Extrema on an Interval
4.2 Rolle's Theorem and the Mean Value Theorem
4.3 Increasing and Decreasing Functions and the First Derivative Test
4.4 Concavity and the Second Derivative Test
4.5 Limits at Infinity
4.6 A Summary of Curve Sketching
4.7 Optimization Problems
4.8 Differentials
Chapter 5 Integration (2-3 weeks)
5.1 Antiderivatives and Indefinite Integration
5.2 Area
5.3 Riemann Sums and Definite Integrals
5.4 The Fundamental Theorem of Calculus
5.5 Integration by Substitution
5.6 Numerical Integration (omit)
5.7 The Natural Logarithmic Function: Integration (omit)
5.8 Inverse Trigonometric Functions: Integration (omit)
5.9 Hyperbolic Functions (omit)
[ Return to Course Descriptions ]