# Department of Mathematics Syllabus

This syllabus is advisory only. For details on a particular instructor's syllabus (including books), consult the instructor's course page. For a list of what courses are being taught each quarter, refer to the Courses page.

MAT 21A: Calculus: Differential Calculus
Approved: 2007-04-01 (revised 2013-01-01, J. DeLoera)

ATTENTION:

This course is part of the inclusive access program, in which your textbook and other course resources will be made available online. Please consult your instructor on the FIRST DAY of instruction.

This course requires the Math Placement Exam. Read More.

Suggested Textbook: (actual textbook varies by instructor; check your instructor)
Thomas' Calculus Early Transcendentals, 14th Edition by George B. Thomas, Maurice Weir, and Joel Hass, Joel; Addison Wesley Publishers.

Prerequisites:

Two years of high school algebra, plane geometry, plane trigonometry, and analytic geometry; Must satisfy the Mathematics Placement Requirement.

Suggested Schedule:

 Lecture(s) Sections Comments/Topics 1 1.1 – 1.6 Review chapter one. Cover definitions of exponential functions, inverse functions, and logarithms. Okay to skip and refer to as needed. 1 2.1 Rates of change and tangents to curves 1 2.2 Limit of a function and limit laws 1 2.3 Precise definition of limit 1 2.4 One-sided limits 1.5 2.5 Continuity 1.5 2.6 Limits involving infinity; asymptotes of graphs 0.5 3.1 Tangents and the derivative at a point 1 3.2 The derivative as a function 1.5 3.3 Differentiation rules 1 3.4 The derivative as a rate of change 0.5 3.5 Derivatives of trigonometric functions 1.5 3.6 The Chain Rule 1 3.7 Implicit differentiation 1 3.8 Derivative of inverse functions and logarithms 1 3.9 Inverse trigonometric functions 1 3.10 Related rates 1 3.11 Linearization and differentials 1 4.1 Extreme values of functions 1 4.2 The Mean Value Theorem 1 4.3 Monotonic functions and the first derivative test 1 4.4 Concavity and curve sketching 1 4.5 Indeterminate forms and L’Hopital’s Rule (omit proof) 1 4.6 Applied optimization 1 4.7 Newton’s method

Total number of lectures = 26. This leaves time for exams and lecture time adjustments. If time seems short consider omitting the review of chapter one and weaving in the material as necessary. If time begins to run out, section 3.9 is lower priority.

Learning Goals:

A goal of this course is to help students develop effective strategies for solving both mathematical and real world problems. Although students often do not like “word problems” probing applications of their mathematical skills, it is very important that instructors emphasize these types of problems so that students become experts at them. In particular, students should be taught how to create mathematical models, develop effective strategies for solving problems in applied settings and non-routine situations.

Students will learn the fundaments of differential calculus. At its most rudimentary level, this is the study of rates of change and motion which enables computations of how systems evolve based on simple laws. Calculus therefore forms the foundations of modern science. In this course student not only learn the basic techniques of calculus, but also how to distill the mathematical essence of real world systems in terms of well posed problems for the important variables of the problem.

This course is an entry point to advance mathematics. Mastery of this course enhances analytic and problem solving skills of students. At the same time the course supports the ability to design mathematical models in a wide range of applied fields.

Assessment:

Their mastery of these course is commonly assessed by quizzes, homework problems, TA led discussion sections and comprehensive examinations.