# 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