Math 125 syllabus

Calculus I

Course Description:  This course provides an introduction to calculus with emphasis on differential calculus. Topics include limits of functions, derivatives of algebraic and transcendental functions, application of the derivative to curve sketching, optimization problems, and examples in the natural sciences, engineering, and economics. The course concludes with an introduction to anti-derivatives, definite integrals, and the fundamental theorem of calculus. Credit for both MA 120 and MA 125 is not allowed.

Core Course  

Prerequisites:  C or better in MA 113 or MA 115, or sufficient mathematics placement test score, or a sufficient ACT Mathematics subscore.  

Textbook:   Joel Hass and Maurice D. Weir: University Calculus Early Transcendentals, (with access code to MyMathLab) Pearson, 3rd edition, 2016 (ISBN 978-0-321-99957-3 (print text) or ISBN 978-0-321-19991-1 (e-text) ). 

 

Learning Objectives:

Upon the successful completion of the course a student will be able to:

  • Compute limits of functions graphically, numerically, and algebraically;
  • Verify using the ε-δ-definition that a given real number is the limit of a function;
  • Compute and interpret the derivative as a rate of change, as a slope, as a linear approximation, and as a tool for optimization problems;
  • Analyze algebraic and transcendental functions with regard to their critical behavior, regions of increase and decrease, concavity properties and asymptotic behavior, and sketch a graph based on these observations;
  • Compute simple anti-derivatives;
  • Estimate an area under a curve and a definite integral using Riemann sums;
  • Interpret a definite integral as a signed area;
  • Sate and use the fundamental theorem of calculus;
  • State and prove results about limits, derivatives, and mean values.

 

Topics & Time Distribution:

By assuming the total of 13 weeks, the instructor is given an extra week and a half to use for tests, emphasis on certain topics, etc. 

Chapter 1 - Functions  (0.5 weeks)

Chapter 2 - Limits and Continuity (3 weeks)

Chapter 3 - Differentiation (3.5 weeks)

Chapter 4 - Applications of Derivatives (4 weeks)

Chapter 5  - Integration (2 weeks)

 

Detailed Schedule:

Below are the essential sections which should be covered by all instructors:

Chapter 1:  1.3, 1.5, 1.6

Chapter 2:  2.2, 2.3, 2.4, 2.5, 2.6

Chapter 3:  3.1, 3.2. 3.3, 3.5, 3.6, 3.7, 3.8, 3.9, 3.10, 3.11

Chapter 4:  4.1, 4.2, 4.3, 4.4, 4.5, 4.6, 4.8

Chapter 5:  5.1, 5.2, 5.3, 5.4

 

Common Homework:

The following exercises should be included into the homework assignments by every instructor.  Each instructor should complement them by exercises of her or his choice. It is not intended that the homework assignments consist only of the exercises below.  The selection below refers to the second edition of the textbook University Calculus Early Transcendentals by Joel Hass, Maurice D. Weir, and George B. Thomas, Jr.

 

Chapter 1:

Section 1.3: 5, 9

Section 1.5: 13, 31

Section 1.6: 31, 47, 67

 

Chapter 2:

Section 2.2: 3, 25, 53

Section 2.3: 11, 17, 59

Section 2.4: 3, 15, 25

Section 2.5: 5, 25, 55

Section 2.6: 1, 9, 17, 103

 

Chapter 3:

Section 3.1: 3, 5, 29

Section 3.2: 31, 37

Section 3.3: 23, 51

Section 3.5: 7, 31

Section 3.6: 15, 99

Section 3.7: 1, 31

Section 3.8: 5, 21, 89

Section 3.9: 21, 41

Section 3.10: 1, 13

Section 3.11: 1, 15

 

Chapter 4:

Section 4.1: 29, 55

Section 4.2: 17, 51

Section 4.3: 7, 15

Section 4.4: 11, 93

Section 4.5: 5, 41

Section 4.6: 3, 15

Section 4.8: 19, 41

 

Chapter 5:

 Section 5.1: 3, 13

Section 5.2: 7, 15, 35, 39

Section 5.3: 9, 65

Section 5.4: 7, 49, 61
 

Remark:  The suggested common homework problems are subject to change and refinement in subsequent semesters.

Last Updated January 6, 2016