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Calculus I

• 1. Limits and Continuity

  • 1.1 Numerical and Graphical Approach to Limits
  • 1.2 Limits: Algebraically
  • 1.3 Limits Involving Infinity; Asymptotes
  • 1.4 Limits and Continuity
  • 1.5 Discontinuity
• 2. Derivatives

  • 2.1 Instantaneous Rates of Change, Derivatives
  • 2.2 Derivatives as Functions
  • 2.3 Basic Differentiation Formulas
  • 2.4 Product Rule, Quotient Rule
  • 2.5 Chain Rule
  • 2.6 Implicit Differentiation
  • 2.7 Related Rates
  • 2.8 Linear Approximation; Differentials
  • 2.9 Derivatives of Inverse Functions, Arcsine, and Arctangent
  • 2.10 Derivatives of Exponential Functions
  • 2.11 Derivatives of Logarithmic Functions
• 3. Applications of Derivatives

  • 3.1 Limits of Ratios of Functions
  • 3.2 Indeterminate Forms and L'Hopital's Rule
  • 3.3 Maximum and Minimum Values (Extrema)
  • 3.4 Mean-Value Theorem
  • 3.5 Derivatives and The Shape of Graphs
  • 3.6 Curve Sketching
  • 3.7 Optimization
• 4. Integrals

  • 4.1 Antiderivatives
  • 4.2 Riemann Sums, Areas and Distances
  • 4.3 Accumulation and the Definite Integral
  • 4.4 Riemann Sums; Evaluating Definite Integrals
  • 4.5 The Fundamental Theorem of Calculus
  • 4.6 Average Value and Mean Value Theorems

Business Calculus

• 1. Limits and Continuity

  • 1.1 Limits: Numerical and Graphical Approaches
  • 1.2 Continuity
• 2. Derivatives and Differentiation

  • 2.1 Average Rate of Change and Derivatives
  • 2.2 Derivatives as Functions
  • 2.3 Differentiation of Powers, Sums and Constant Multiples
  • 2.4 Product and Quotient Rules
  • 2.5 Chain Rule
  • 2.6 Derivatives of Logarithmic and Exponential Functions
  • 2.7 Implicit Differentiation
  • 2.8 Related Rates
  • 2.9 Higher-order Derivatives: Acceleration and Concavity
• 3. Applications of Derivatives

  • 3.1 Marginal Analysis
  • 3.2 Maxima and Minima
  • 3.3 Applications of Maxima and Minima
  • 3.4 Elasticity
• 4. Integration

  • 4.1 The Indefinite Integral
  • 4.2 The Definite Integral: Numerical and Graphical Viewpoints
  • 4.3 Fundamental Theorem of Calculus
  • 4.4 Integration by Parts
  • 4.5 Improper Integrals
• 5. Applications of Integration

  • 5.1 Area Between Two Curves
  • 5.2 Averages and Moving Averages
  • 5.3 Applications to Business and Economics

College Algebra

• 1. Algebra Essentials

  • 1.1 The Real Line
  • 1.2 Exponents and Radicals
  • 1.3 The Absolute Value
  • 1.4 Factoring Polynomial Expressions
  • 1.5 Completing the Square
  • 1.6 Rational Expressions
  • 1.7 Complex Numbers
• 2. Equations and Inequalities

  • 2.1 Linear Equations
  • 2.2 Quadratic Equations
  • 2.3 The Quadratic Formula
  • 2.4 Introduction to Inequalities
• 3. Functions

  • 3.1 What is a function?
  • 3.2 Domain and Range
  • 3.3 The Graph of a function
  • 3.4 Adding, multiplying, and composing functions
  • 3.5 Inverse functions
  • 3.6 Finding inverse functions algebraically
• 4. Linear Functions

  • 4.1 Introduction to Linear Functions
  • 4.2 Constructing Linear Functions
  • 4.3 Modeling with Linear Functions
• 5. Polynomials and Rational Functions

  • 5.1 Introduction to Polynomials
  • 5.2.1 Zeros of Polynomials: Rational Zero Theorem, Constructing Polynomials
  • 5.2.2 Zeros of Polynomials: Remainder and Factor Theorem
  • 5.2.3 Zeros of Polynomials: Descartes' Rule, Complex Roots, Applications
  • 5.3 Rational Functions
  • 5.4 Polynomials division
• 6. Exponentials and logs

  • 6.1 Exponential Functions
  • 6.2 The Base e
  • 6.3 Logarithmic Functions
  • 6.4 Properties of Logarithms
  • 6.5 Modeling with Logarithms
• 7. Systems of Linear Equations

  • 7.1 Linear Systems in Two Variables
  • 7.2 Linear Systems in Three Variables
  • 7.3 Systems of nonlinear Equations
  • 7.4 Systems of linear inequalities
• 8. Trigonometry
• 9. Conics