MATH 125 Section 003: Calculus I

A grade of C- or higher in MATH 112 and MATH 113 (or MATH 115) or a mathematics placement score in the 440-600 range.

First course in the three part basic calculus sequence for students majoring in mathematics, science, or engineering. Topics include limits, continuity, differentiation, applications of differentiation, and integration. Applications of the derivative are covered in detail, including approximations of errors using differentials, maxima and minima problems, curve sketching, optimization problems, and Newton's Method. Topics on integration include Riemann sums, properties of definite integrals, integration by substitution, and integrals involving logarithmic, exponential, trigonometric, inverse trigonometric, and hyperbolic functions.

1. Students will develop a basic understanding of the concepts of calculus and be able to apply them to real situations.
2. Students will be able to find limits of functions.
3. Students will be able to calculate (and simplify) derivatives involving rational, exponential, trigonometric, inverse trigonometric, and hyperbolic functions.
4. Students will be able to apply derivatives to various applications including optimization problems, linear approximation, and curve sketching.
5. Students will be able to calculate (and simplify) integrals using some basic techniques of integration.
6. Students will be able to use integration to find the area of certain types of planar regions.

CHAPTERS COVERED:

1          Functions and Limits*

2          Derivatives (Section 2.7 is optional and will not be covered.)

3          Inverse Functions: Exponential, Logarithmic, and Inverse Trigonometric Functions

               (Section 3.4 is optional and will not be covered, section 3.7 omit)

4          Applications of Differentiation

5          Integrals

7          Applications of Integration (Cover section 7.1 only:  Areas Between Curves)

* The material covered on pages 1 – 23 is a brief review of pre-calculus mathematics.  Students who are not familiar with this review material need to take MATH 112 and MATH 113 (or MATH 115) before attempting MATH 125.

TEST MATERIAL: Test problems will be similar to the assigned exercises.  The assigned exercises cover all material that will appear on the tests.  Students should keep their solutions to homework problems in a notebook that can be reviewed when studying for examinations.

SECTIONS TO BE COVERED                                 PAGE  ASSIGNED EXERCISES

 1.3 The Limit of a Function                                      33         3, 4, 5, 11, 13, 15, 18, 20, 22, 23, 24, 25

1.4 Calculating Limits                                                43         11, 13, 15, 17, 21, 23, 24, 25, 29, 30, 33

35, 38, 39, 40, 41, 43, 45

1.5 Continuity                                                               54         3, 7, 13, 15, 21, 27, 29, 31, 32

1.6 Limits Involving Infinity                                         66         1, 2, 13, 14, 15, 17, 19, 21, 22, 23, 27, 32

2.1 Derivatives and Rates of Change                     80         3, 5, 19, 21, 23, 25, 27, 47, 48

2.2 The Derivative as a Function                              91         3, 17, 19, 21, 23, 31, 32

Test 1          Thursday, September 15       Covers all material from sections 1.3 through 2.2   

SECTIONS TO BE COVERED                                 PAGE  ASSIGNED EXERCISES

2.3 Basic Differentiation Formulas                       104       1, 3, 5, 7, 9, 11, 13, 15, 17, 25, 26, 46, 47

2.4 The Product and Quotient Rules                   111       3, 4, 7, 11, 16, 19, 23, 27, 28, 41, 42

2.5 The Chain Rule                                                119       1, 3, 5, 7, 9, 13, 19, 21, 27, 29, 30, 31, 39, 41

2.6 Implicit Differentiation                                     125       3, 5, 7, 9, 13, 17, 18, 27, 28, 39

2.7 Related Rates (OMIT)

2.8 Linear Approximations and Differentials  137       1, 3, 5, 6, 7, 17, 19

3.1 Exponential Functions                                  147       7, 9, 11, 13, 15, 17, 23, 25, 27

3.2 Inverse Functions and Logarithms            158       5, 7, 9, 11, 15, 17, 21, 23, 25, 31, 33, 35, 43,

45, 47, 51, 53, 61, 63

3.3 Derivatives of Log and Exponent Function  166      1,3, 5, 7, 17, 19, 21, 23, 25, 31, 35, 42, 49, 51

3.4 Exponential Growth and Decay (OMIT)

Test 2         Tuesday, October, 11          Covers all of the above material from sections 2.3 through 3.4

SECTIONS TO BE COVERED                                 PAGE  ASSIGNED EXERCISES

 3.5 Inverse Trigonometric Functions                   180       1, 3, 5, 7, 9, 17, 19, 21, 23, 25

3.6 Hyperbolic Functions                                        185       27, 29, 33, 35, 36, 37, 43

3.7 L’Hospitals Rule (OMIT) This section will be covered in Calculus II

4.1 Maximum and Minimum Values                     203       3, 5, 15, 17, 21, 23, 25, 35, 37, 39, 41, 43

4.2 The Mean Value Theorem                               210       1, 4, 5, 11, 12, 14, 16, 23, 24, 25, 32, 33

4.3 Derivatives and The Shapes of Graphs       217       1, 3, 5, 7, 23, 25, 27, 29, 31

4.4 Curve Sketching                                               225       5, 9, 15, 19, 23

4.5 Optimization Problems                                   232       7, 9, 10, 13, 16, 17, 19, 46

4.6 Newton’s Method                                             240       5, 7, 9, 11

Test 3          Thursday, November 3       Covers the above material from sections 3.5 through 4.6

 SECTIONS TO BE COVERED                                 PAGE  ASSIGNED EXERCISES

4.7 Antiderivatives                                                     246       1, 3, 5, 7, 9, 13, 19, 23, 27

5.1 Areas and Distances                                         260       1, 3, 5, 13, 15, 16

5.2 The Definite Integral                                          272       1, 3, 11, 13, 15, 21, 29, 30, 31, 33, 35

5.3 Evaluating Definite Integrals                           282       1, 5, 9, 13, 15, 17, 19, 23, 27, 29, 31

35, 42, 43, 44, 45, 46

5.4 The Fundamental Theorem of Calculus      291       5, 6, 7, 8, 9, 10, 11, 12, 31

5.5 The Substitution Rule                                      298       1, 3, 5, 7, 9, 11, 13, 19, 21, 25, 27, 33,

                                                                                                36, 37, 38, 41, 43, 61, 62, 65

7.1 The Area Between Curves                              361       1, 2, 3, 5, 7, 9, 11, 12, 15

Test 4    Thursday, December 1    Covers all of the above material from sections 4.7 through 5.5 and 7.1

 Comprehensive Final Exam        Wednesday, December 14         11:30 AM – 2:00 PM 

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