ModelCourses/Differential Calculus

Problem sets

• Set 01 Functions and Change Students will be able to
  • Find equations of lines
  • Find equations of perpendicular lines
  • Find equations of parallel lines
  • Find the domain and range of functions

• Set 02 Exponential Functions Students will be able to
  • Construct exponential functions based on given numerical data
  • Construct exponential functions based on given graphical data
  • Find the concavity of a function based on graphical data

• Set 03 New Functions from Old
• Set 04 Logarithmic Functions
• Set 05 Trigonometric Functions
• Set 06 Powers, Polynomials, and Rational Functions
• Set 07 Introduction to Continuity
• Set 08 Limits
• Set 09 Introduction to the derivative
• Set 10 The Derivative at a Point
• Set 11 The Derivative Function
• Set 12 Interpretations of the Derivative
• Set 13 The Second Derivative
• Set 14 Differentiability
• Set 15 Powers and Polynomials
• Set 16 The Exponential Function
• Set 17 The Product and Quotient Rules
• Set 18 The Chain Rule
• Set 19 The Trigonometric Functions
• Set 20 The Chain Rule and Inverse Functions
• Set 21 Implicit Functions
• Set 22 Hyperbolic Functions
• Set 23 Linear Approximation and the Derivative
• Set 24 Theorems about Differentiable Functions
• Set 25 Using First and Second Derivatives
• Set 26 Optimization
• Set 27 Families of Functions
• Set 28 Optimization Geometry and Modeling
• Set 29 Applications to Marginality (optional)
• Set 30 Rates and Related Rates
• Set 31 L’Hopital’s Rule, Growth, and Dominance
• Set 32 Parametric Equations
• Set 33 Introduction to the definite integral
• Set 34 The Definite Integral
• Set 35 The Fundamental Theorem and Interpretations
• Set 36 Theorems about Definite Integrals
• Set 37 Antiderivatives Graphically and Numerically
• Set 38 Constructing Antiderivatives Analytically
• Set 39 Differential Equations
• Set 40 Second Fundamental Theorem of Calculus
• Set 41 The Equations of Motion