Mathematics (1) - Calculus (BSCS101)

Course includes the following lectures:

0- Preliminaries

• The Real Numbers and the Cartesian Plane

• Lines and Functions

• Trigonometric Functions

• Transformations of Functions

  1- Limits and Conntinouty

• The Concept of Limit

• Computation of Limits

• Continuity and Its Consequences

• Limits Involving Infinity; Asymptotes

2- Differentiation

• Tangent Lines and Velocity

• The Derivative

• Computation of Derivatives: The Power Rule 2,4 The Product and Quotient Rules

• The Chain Rule

• Derivatives of Trigonometric Functions

• Implicit Differentiation

• The Mean Value Theorem

3- Applications of Differentiation

• Linear Approximations

• Maximum and Minimum Values

• Increasing and Decreasing Functions

• Concavity and the Second Derivative Test

• Overview of Curve Sketching

• Optimization

• Related Rates

4- Integration 

• Antiderivatives

• Sums and Sigma Notation

• Area

• The Definite Integral

• The Fundamental Theorem of Calculus

• Integration by Substitution

• Numerical Integration

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