2. Outlook: Content of the Course

 

  • 1. Functions
    • 1.1. Linear and Quadratic Functions
    • 1.2. Power Functions, Polynomials and Power Series
    • 1.3. The Exponential Function and Growth
    • 1.4. Trigonometric Functions
    • 1.5. Multivariable Functions
    • 1.6. Curves and Maps
    • 1.7. Exercises
  • 2. Equations
    • 2.1. Basic Concepts and Solving Methods
    • 2.2. Linear and Quadratic Equations
    • 2.3. Trigonometric Equations
    • 2.4. Exponential and Logarithmic Equations
    • 2.5. Complex numbers
    • 2.6. Exercises
  • 3. Sequences and Limits
    • 3.1. Introduction to sequences
    • 3.2. Different ways of defining a sequence
    • 3.3. Important examples of sequences
    • 3.4. Basic properties of sequences
    • 3.5. Limit of a function
    • 3.6. Operations with limits
    • 3.7. Continuity of a function
    • 3.8. Properties of continuous functions
    • 3.9. Exercises
  • 4. Differentiation
    • 4.1. Derivative
    • 4.2. Properties of derivative
    • 4.3. Derivatives of Trigonometric Functions
    • 4.4. The Chain Rule
    • 4.5. The Exponential Function and the Logarithm
    • 4.6. Extremal Value Problems
    • 4.7. Exercices
  • 5. Integration
    • 5.1. The Concept
    • 5.2. Fundamental theorem of calculus
    • 5.3. Integrals of elementary functions
    • 5.4. Integration techniques
    • 5.5. Applications
    • 5.6. Exercises
  • 6. Differential Equations
    • 6.1. Differential Equation
    • 6.2. Solving a 1st order ODE
    • 6.3. 2nd and higher order ODEs
    • 6.4. Exercises