MAC 2241 — Life Sciences Calculus I — Syllabus
Prerequisites: C (2.0) or better in MAC 1114, 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 has two different formats: daytime
sections have three 50-minute lectures per week and two 50-minute help sessions;
evening sections have two 110-minute lectures per week. Successful completion of
the course merits 4 semester hours of credit. 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 for Biology and Medicine, 2nd Edition, by C.
Neuhauser
Course Content
Chapter 1: Preview and Review (This chapter is a review and not covered.)
1.1 Preliminaries
1.2 Elementary Functions
1.3 Graphing
Chapter 2: Discrete Time Models, Sequences, and Difference Equations
(one week)
2.1 Exponential Growth and Decay (omit)
2.1.1 Modeling Population Growth in Discrete Time
2.1.2 Recursions
2.2 Sequences
2.2.1 What Are Sequences?
2.2.2 Limits
2.2.3 Recursions
2.3 More Population Models (omit)
2.3.1 Restricted Population Growth: The Beverton-Holt Recruitment Curve
2.3.2 The Discrete Logistic Equation
2.3.3 Ricker's Curve
2.3.4 Fibonacci Sequences
Chapter 3: Limits and Continuity (2-3 weeks)
3.1 Limits
3.1.1 An Informal Discussion of Limits
3.1.2 Limit Laws
3.2 Continuity
3.2.1 What is Continuity?
3.2.2 Combinations of Continuous Functions
3.3 Limits at Infinity
3.4 The Sandwich Theorem and Some Trigonometric Limits
3.5 Properties of Continuous Functions
3.5.1 The Intermediate Value Theorem
3.5.2 A Final Remark on Continuous Functions
3.6 A Formal Definition of Limits (omit)
Chapter 4: Differentiation (4-5 weeks)
4.1 Formal Definition of the Derivative
4.1.1 Geometric Interpretation and Using the Definition
4.1.2 The Derivative as an Instantaneous Rate of Change: A First Look at
Differential Equations
4.1.3 Differentiability and Continuity
4.2 The Power Rule, the Basic Rules of Differentiation, and the Derivatives of
Polynomials
4.3 The Product and Quotient Rules, and the Derivatives of Rational and Power
Functions
4.3.1 The Product Rule
4.3.2 The Quotient Rule
4.4 The Chain Rule and Higher Derivatives
4.4.1 The Chain Rule
4.4.2 Implicit Functions and Implicit Differentiation
4.4.3 Related Rates
4.4.4 Higher Derivatives
4.5 Derivatives of Trigonometric Functions
4.6 Derivatives of Exponential Functions
4.7 Derivatives of Inverse and Logarithmic Functions
4.7.1 Derivatives of Inverse Functions
4.7.2 The Derivative of the Logarithmic Function
4.7.3 Logarithmic Differentiation
4.8 Approximation and Local Linearity
Chapter 5: Applications of Differentiation (3-4 weeks)
5.1 Extrema and the Mean Value Theorem
5.1.1 The Extreme Value Theorem
5.1.2 Local Extrema
5.1.3 The Mean Value Theorem
5.2 Monotonicity and Concavity
5.2.1 Monotonicity
5.2.2 Concavity
5.3 Extrema, Inflection Points, and Graphing
5.3.1 Extrema
5.3.2 Inflection Points
5.3.3 Graphing and Asymptotes
5.4 Optimization
5.5 L'Hospital's Rule
5.6 Difference Equations: Stability (omit)
5.6.1 Exponential Growth
5.6.2 Stability: General Case
5.6.3 Examples
5.7 Numerical Methods: The Newton-Raphson Method (omit)
5.8 Antiderivatives
Chapter 6: Integration (2-3 weeks)
6.1 The Definite Integral
6.1.1 The Area Problem
6.1.2 Riemann Integrals
6.1.3 Properties of the Riemann Integral
6.2 The Fundamental Theorem of Calculus
6.2.1 The Fundamental Theorem of Calculus (Part I)
6.2.2 Antiderivatives and Indefinite Integrals
6.2.3 The Fundamental Theorem of Calculus (Part II)
6.3 Applications of Integration
6.3.1 Areas
6.3.2 Cumulative Change
6.3.3 Average Values
6.3.4 The Volume of a Solid (omit)
6.3.5 Rectification of Curves (omit)
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