Demokurs: Introduction to Engineering Mathematics

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