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MATH 165. Calculus I.
(4-0) Cr. 4. F.S.SS. Prereq: Satisfactory performance on placement exam, 2 years of high school algebra, 1 year of geometry, 1 semester of trigonometry.
Differential calculus, applications of the derivative, introduction to integral calculus. Only one of Math 151 or 160 or the sequence MATH 165-MATH 166, or the sequence MATH 181-MATH 182 may be counted towards graduation.
MATH 166. Calculus II.
(4-0) Cr. 4. F.S.SS. Prereq: Minimum of C- in MATH 165 or high math placement scores.
Integral calculus, applications of the integral, infinite series. Only one of MATH 151, MATH 160, the sequence MATH 165-MATH 166, or the sequence MATH 181-MATH 182 may be counted towards graduation.
Thomas' Calculus, Early Transcendentals, 12th Edition.
Chapter and Section references are to Thomas' Calculus, Early Transcendentals, 12th ed.
Times for both courses are suggested based on a 15-week semester of 59 class meetings, allowing 9 days for review and exams.
Chapter 1 is a review of high school mathematics; Math 165 begins with Chapter 2.
|Course||Chapter & Sections Topics||Time|
|Math 165||Chapter 2 - Limits and Continuity||9 days|
|§2.1 - Rates of Change and Tangents
§2.2 - Limits of Functions and Limit Laws
§2.3 - Precise Definition of a Limit (Optional)
§2.4 - One-Sided Limits
§2.5 - Continuity
§2.6 - Limits Involving Infinity, Asymptotes
|Chapter 3 - Differentiation||16 days|
|§3.1 Tangents and the Derivative
§3.2 The Derivative as a Function
§3.3 Differentiation Rules
§3.4 The Derivative as a Rate of Change
§3.5 Derivatives of Trigonometric Functions
§3.6 The Chain Rule
§3.7 Implicit Differentiation
§3.8 Derivatives of Inverse Functions and Logarithms
§3.9 Inverse Trogonometric Functions
§3.10 Related Rates
§3.11 Linearization and Differentials
|Chapter 4 - Applications of Derivatives||11 days|
|§4.1 - Extreme Values
§4.2 - Mean Value Theorem (Optional)
§4.3 - Monotonic Functions, First Derivative Test
§4.4 - Concavity
§4.6 - Optimization
§4.7 - Newton's Method
§4.8 - Antiderivatives
|Chapter 5 - Integration||11 days|
|§5.1 - Area and Estimating with Finite Sums
§5.2 - Sigma Notation and Limits of Finite Sums
§5.3 - The Definite Integral
§5.4 - The Fundamental Theorem of Calculus
§5.5 - Indefinite Integrals and Substituion
§5.6 - Substitution and Area Between Curves
|Chapter 7 - Integrals and Transcendental Functions||3 days|
|§7.1 The Logarigthm Defined as an Integral (Optional)
§7.2 Exponential Change and Separable Differential Equations
§7.3 - Hyperbolic Functions (Optional)
§4.5 - L'Hôpital's Rule
§7.4 - Relative Rates of Growth (Optional)
|Math 166||Chapter 6 - Applications of Definite Integrals||12 days|
|§6.1 - Volumes Using Cross-sections
§6.2 - Volumes Using Cylindrical Shells
§6.3 - Arc Length
§6.4 - Areas of Surfaces of Revolution
§6.5 - Work and Fluid Forces
§6.6 - Moments and Centers of Mass
|Chapter 8 - Techniques of Integration||12 days|
|§8.1 - Integration by Parts
§8.2 - Trigonmetric Integrals
§8.3 - Trigonometric Substitutions
§8.4 - Integration of Rational Functions by Partial Fractions
§8.5 - Integral Tables and Computer Algebra Systems (Optional)
§8.6 - Numerical Integration
§8.7 - Improper Integrals
|Chapter 10 - Infinite Sequences and Series||17 days|
|§10.1 - Sequences
§10.2 - Infinite Series
§10.3 - The Integral Test
§10.4 - Comparison Tests
§10.5 - The Ratio and Root Tests
§10.6 - Alternating Series, Absolute and Conditional Convergence
§10.7 - Power Series
§10.8 - Taylor and McLaurin Series
§10.9 - Convergence of Taylor Series
§10.10 - The Binomial Series and Applications of Taylor Series
|Chapter 11 - Parametric Equations and Polar Coordinates||9 days|
|§11.1 - Parametrizations of Plane Curves
§11.2 - Calculus with Parametric Curves
§11.3 - Polar Coordinates
§11.4 - Graphing in Polar Coordinates
§11.5 - Areas and Lengths in Polar Coordinates
Math 165 Learning Objectives
Math 166 Learning Objectives
Old Exams for Math 165
Old Exams for Math 166
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