Calculus 1

Course Info

Table of Contents

Chapter P – PREPARATION FOR CALCULUS

  • P.1  Graphs and Models
  • P.2  Linear Models and Rates of Change
  • P.3  Functions and Their Graphs
  • P.4  Fitting Models to Data

Chapter 1 – LIMITS AND THEIR PROPERTIES

  • 1.1  A Preview of Calculus
  • 1.2  Finding Limits Graphically and Numerically
  • 1.3  Evaluating Limits Analytically
  • 1.4  Continuity and One-Sided Limits
  • 1.5  Infinite Limits

Chapter 2 – DIFFERENTIATION

  • 2.1  The Derivative and the Tangent Line Problem
  • 2.2  Basic Differentiation Rules and Rates of Change
  • 2.3  The Product and Quotient Rules and Higher-Order Derivatives
  • 2.4  The Chain Rule
  • 2.5  Implicit Differentiation
  • 2.6  Related Rates

Chapter 3 – APPLICATIONS OF DIFFERENTIATION

  • 3.1  Extrema on an Interval
  • 3.2  Rolle’s Theorem and the Mean Value Theorem
  • 3.3  Increasing and Decreasing Functions and the First Derivative Test
  • 3.4  Concavity and the Second Derivative Test
  • 3.5  Limits at Infinity
  • 3.6  A Summary of Curve Sketching
  • 3.7  Optimization Problems
  • 3.8  Newton’s Method
  • 3.9  Differentials

 

Chapter 4 – INTEGRATION

  • 4.1  Antiderivatives and Indefinite Integration
  • 4.2  Area
  • 4.3  Riemann Sums and Definite Integrals
  • 4.4  The Fundamental Theorem of Calculus
  • 4.5  Integration by Substitution
  • 4.6  Numerical Integration

Chapter 5 – LOGARITHMIC, EXPONENTIAL, AND OTHER TRANSCENDENTAL FUNCTIONS

  • 5.1  The Natural Logarithmic Function: Differentiation
  • 5.2  The Natural Logarithmic Function: Integration
  • 5.3  Inverse Functions
  • 5.4  Exponential Functions: Differentiation and Integration
  • 5.5  Bases Other than e and Applications
  • 5.6  Inverse Trigonometric Functions: Differentiation
  • 5.7  Inverse Trigonometric Functions: Integration
  • 5.8  Hyperbolic Functions

Chapter 6 – DIFFERENTIAL EQUATIONS

  • 6.1  Slope Fields and Euler’s Method
  • 6.2  Differential Equations: Growth and Decay
  • 6.3  Separation of Variables and the Logistic Equation
  • 6.4  First-Order Linear Differential Equations

 

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