## Math 234. Calculus for Business I

Lecture Syllabus

**Textbook:** Hoffmann and Bradley, Calculus For Business, Economics, and the Social and Life Sciences, 11th Edition

### 1 Functions, Graphs, and Limits (4 lectures)

1.1 Functions

1.2 The Graph of a Function

1.3 Linear Functions

1.5 Limits

1.6 One-Sided Limits and Continuity

### 2 Differentiation: Basic Concepts (5 lectures)

2.1 The Derivative

2.2 Techniques of Differentiation

2.3 Product and Quotient Rules; Higher-Order Derivatives

2.4 The Chain Rule

2.5 Marginal Analysis and Approximations Using Increments

2.6 Implicit Differentiation and Related Rates

### 3 Additional Appilcations of the Derivative (4 lectures)

3.1 Increasing and Decreasing Functions; Relative Extrema

3.2 Concavity and Points of Inflection

3.3 Curve Sketching

3.4 Optimization

3.5 Additional Applied Optimization

### 4 Exponential and Logarithmic Functions (3.5 lectures)

4.1 Exponential Functions

4.2 Logarithmic Functions

4.3 Differentiation of Logarithmic and Exponential Functions

4.4 Additional Exponential Models

### 5 Integration (3.5 lectures)

5.1 Antidifferentiation: The Indefinite Integral

5.2 Integration by Substitution

5.3 The Definite Integral and the Fundamental Theorem of Calculus

5.4 Applying Definite Integration: Area Between Curves and Average Value

5.5 Additional Applications to Business and Economics

### 6 Additional Topics in Integration (1 lectures)

6.1 Integration by Parts (Do not include Integral Tables)

### 7 Calculus of Several Variables (4 lectures)

7.1 Functions of Several Variables

7.2 Partial Derivatives

7.3 Optimizing Functions of Two Variables

7.5 Constrained Optimization: The Method of Lagrange Multipliers

7.6 Double Integrals (if time permits)

### Hour Exams (3 class periods)

### Leeway (0 class periods)

Remarks:

- Either Section 1.1 or 1.2 should be covered during the first meeting of the Discussion Sections. Otherwise, Discussion Sections should be used for doing problems on the board.
- Homework and/or a quiz should be given and graded in each non-exam week. Regular feedback is essential!
- At least three hours exams should be given. The syllabus above indicates a suggestion for three exams. If four hour tests are desired, an approach might be to place Test #3 after Integration and Test #4 after Chapter 7.
- No knowledge of trigonometry can be assumed.
- This course is intended primarily for students in commerce and the social sciences. Emphasis should be placed on techniques and applications, not on theoretical aspects. The examples should, whenever possible, be taken from relevant fields.