MATH 215: Applied Calculus I (Summer 2023)

Instructor: Nha Truong

Office hours: MW 12:30-2:00 PM - Keller 410

Course information:

Time: MWF 10:30 AM - 12:15 PM

Room:  Keller 401 

Textbook: Biocalculus, Calculus, Probabliity and Statistics for the Life Sciences by James Stewart and Troy Day.

Grade: Quiz (20%), Homework(20%), Midterm  (June 30, July 28) (30%), Final (Aug 11) (30%).

Syllabus: For more details, please read the syllabus. 

Click here for the lecture notes

Homework:

Chapter 1: 34,36 (page 15) 47 (page 16), 13 (page 29), 42(page 39), 30 (page 51), 49 a,b (page 66)

Chapter 2: 9,13,17 (page 99), 8,16(page 110), 36 (page 124), 19(page 148)

Chapter 3: 5 (page 165), 26 (page 180), 7,10, 33 (page 192), 4,17(page 200), 7,11,26 (page 212)

Chapter 4: 26, 39 (page 257), 30 a,b,d (page 272), 6(page 293).

Chapter 5: 19, 22, (page 340),6, 12, 18, 45 (page 350-351), 2,5,19 (page 360), 4,6,21 (page 367)  3,5(page 370) 3,4,7(page 380)

Chapter 6: 3,6 ,8 (page 392-3), 13,15 (page 400), 1,2,5(page 411)

Schedule

1. Introduction to functions:

1.1 Four ways to represent a function

1.2 Essential functions

1.3 New functions from old function

1.4 Exponential Functions

1.5 Logarithms 

2. Limits 

2.1 Limits of Sequences

2.2 Limit of Functions at Infinity

2.3 Limit of Functions at Finite Numbers.

2.4. Continuity

3. Differentiation:

3.1 Derivatives and Rates of Changes

3.2 The derivatives as a function

3.3 Basic Differentiation Formulas

3.4 The Product and Quotient Rules

3.5 The Chain Rule

3.7 Derivative of the Logarithmic and Inverse Tangent Functions

4. Applications of Derivatives

4.1 Maximum and Minimmum Values

4.2 The Shape of a Graph

4.3 Optimization Problems. 

5. Integration:

5.1 Areas and Distances

5.2 The Definite Integral

5.3 The Fundematal Theorem of Calculus

5.4 The Subsitution Rule

5.5 Integration by Parts

5.6 Partial Fractions

5.7 Improper Integrals

6. Application of Integration

6.1 Area between curves

6.2 Average Values

6.3 Volumes

7. Differential Equations:

7.1 Modeling with Differential Equations

7.2 Direction Fields and Euler's Method

7.3 Separable Equations