# MATH 160 Survey of Calculus

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1 MATH 160 Survey of Calculus

2 Course Guide Self-paced study. Anytime. Anywhere! Mathematics 160 Survey of Calculus University of Idaho 4 Semester-Hour Credits Prepared by: Dusty E. Sabo, Ph.D. Associate Professor of Mathematics Southern Oregon University RV: 1/05 2 -Math 160 Copyright Independent Study in Idaho/Idaho State Board of Education

3 Table of Contents Welcome!... 1 Policies and Procedures... 1 Course Description... 1 Course Materials... 1 Course Delivery... 2 Course Introduction... 2 Course Objectives... 2 Lessons... 2 Exams... 3 Grading... 4 About the Course Developer... 4 Contacting Your Instructor... 4 Assignment Submission Log... 5 Lesson 1: Self-Study: Preliminary Concepts Sections 0.1, Lesson 2: Preliminary Concepts, Continued Sections 0.3, 0.4, Lesson 3: Slopes of Straight and Curved Lines Sections 1.1, Lesson 4: Derivatives and Limits Sections 1.3, Lesson 5: Continuity and Differentiability Sections 1.5, Lesson 6: Derivatives, Continued Sections 1.7, Lesson 7: Self-Study: Review for Exam Exam 1 Information: Covers Lessons Lesson 8: Self-Study: Derivatives and Graphs of Functions Sections 2.1, Lesson 9: Sketching the Graphs of Functions Sections 2.3, Lesson 10: Optimization Problems Sections Lesson 11: Further Optimization Problems Section Lesson 12: Applications of Calculus Section Lesson 13: Differentiation Techniques Sections 3.1, Lesson 14: Self-Study: Review for Exam Exam 2 Information: Covers Lessons Lesson 15: Transcendental Functions Sections 4.1, Lesson 16: Differentiation of Exponential Functions Section Lesson 17: The Natural Logarithm Function Sections 4.4, Lesson 18: Properties of the Natural Logarithm Function Section Lesson 19: Exponential Growth and Decay Section Lesson 20: Self-Study: Compound Interest Section Lesson 21: Self-Study: Review for Exam Exam 3 Information: Covers Lessons Lesson 22: Antidifferentiation Section Lesson 23: Definite Integrals and the Fundamental Theorem Section Lesson 24: Self-Study: Areas in the xy-plane Section Lesson 25: Techniques of Integration Section Lesson 26: Partial Derivatives Sections 7.1,

4 Lesson 27: Relative Maxima and Relative Minima of Functions of Several Variables Sections 7.3, Lesson 28: Self-Study: Review for Exam Exam 4 Information: Covers Lessons Final Exam Information: Covers Lessons

9 Assignment Submission Log Lesson Chapter Reading Written Assignment Date Submitted 1 0 Sections 0.1, 0.2 assigned problems self-study 2 0 Sections 0.3, 0.4, 0.5 assigned problems 3 1 Sections 1.1, 1.2 assigned problems 4 1 Sections 1.3, 1.4 assigned problems 5 1 Sections 1.5, 1.6 assigned problems 6 1 Sections 1.7, 1.8 assigned problems 7 0, 1 Review assigned problems self-study It is time to make arrangements with your proctor to take Exam Sections 2.1, 2.2 assigned problems self-study 9 2 Sections 2.3, 2.4 assigned problems 10 2 Section 2.5 assigned problems 11 2 Section 2.6 assigned problems 12 2 Section 2.7 assigned problems 13 3 Sections 3.1, 3.2 assigned problems 14 2, 3 Review assigned problems self-study It is time to make arrangements with your proctor to take Exam 2. 5

10 15 4 Sections 4.1, 4.2 assigned problems 16 4 Section 4.3 assigned problems 17 4 Sections 4.4, 4.5 assigned problems 18 4 Section 4.6 assigned problems 19 5 Section 5.1 assigned problems 20 5 Section 5.2 assigned problems self-study 21 4, 5 Review assigned problems self-study It is time to make arrangements with your proctor to take Exam Section 6.1 assigned problems 23 6 Section 6.3 assigned problems 24 6 Section 6.4 assigned problems self-study 25 6 Section 6.6 assigned problems 26 7 Sections 7.1, 7.2 assigned problems 27 7 Sections 7.3, 7.4 assigned problems 28 6, 7 Review assigned problems self-study It is time to make arrangements with your proctor to take Exam 4. It is time to make arrangements with your proctor to take the Final Exam. 6

11 Lesson 1 Self-Study: Preliminary Concepts Do not submit this lesson for grading. After carefully working through the following questions, check your answers with the solutions found in the textbook. Reading Assignments Chapter 0, Section 0.1, pp. 3-15; Section 0.2, pp Introduction This course begins with a review of some of the fundamental concepts needed for the study of calculus. This first lesson explores the concept of a function, functional notation, and the graph of a function. Comments These sections briefly review the concept of a function. The importance of being able to use and understand function notation throughout this course cannot be overstated. In particular, note at the bottom of page 7 the use of the convention in higher mathematics that if the domain of a function is not explicitly stated, it is implied to consist of all numbers for which the formula defining the function makes sense. For this class s needs, domains of the functions will always be restricted to subsets of the real numbers. For example, making sense means that mathematically excluded from our domains are numbers yielding division by zero, or numbers requiring the square root of negative numbers. Make these exclusions, as only on occasion will they be explicitly stated. Making sense means even more with regard to word problems where mathematical modes are created for real-world situations. Restrict domains not only to numbers that make mathematical sense, but also to those numbers that are reasonable in the context of the problem. Frequently, numbers that make mathematical sense do not make sense as the solutions to problems which represent real-life situations, such as determining optimal production levels in a factory. Mathematically, a formula may result in the numbers -150 and 200. Eliminate -150 since, in most cases, production levels are not thought of in negative terms. In Section 0.2, pay particular attention to the discussion of linear functions. The ability to understand the algebra of straight lines is important to understanding the notion of a derivative found in calculus. Self-Study Assignments Section 0.1: 13, 15, 17, 19, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 47, 53 (pp ). Section 0.2: 1, 3, 7, 9, 17, 21, 29 (pp ). Checklist Lesson 1 Chapter 0, Section 0.1 Function Value of a function Domain of a function Graph of a function Vertical line test 7

12 Chapter 0, Section 0.2 Linear function Constant function x- and y-intercepts Quadratic function Polynomial function Power function Absolute value function 8

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