Topic outline

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  General

  • Second Semester Calculus-2025 Forum
  • Dear students,

    Please be informed that due to your absence, the lectures will not be delivered again. You are responsible for the material covered and for ensuring that you catch up on any missed content. Please make sure to review the resources available or reach out to your classmates for updates.

    
    

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  Derivatives

  • Lectures 1-2 (Derivatives) File

    Here are the lectures for this week.
    

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  Applications of Derivatives

  • Lecture 3 File

    Here is the lectures for 16/03/2025.
    

  • Lecture 3-Detailed Version File

    Clear version

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  Rolle and Mean Value Theorems With Some Applications

  • Lecture 4 File

    Some Applications on Rolle and Mean Value Theorems are given.

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  Integrations (Definite and Indefinite)

  • Lecture 1-2 File

    This lecture contains the definitions of definite and indefinite integrations along side  some basic properties. It also covers the fundamental theorem of calculus (the two versions).

  • Fundamental Theorem of Calculus (Clear) File
  • Riemann Sum and Area (Examples) File
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  Techniques of Integration

  • Lecture 3-4 File

    This lecture covers  u-substitution method (udu), integration by parts (udv), and trigonometric integration.

  • integral sin^n(x) File
  • Lecture 5- Trigonometric Subtitutions File
  • Integration of Rational Functions File

    Integration of rational functions can be divided into two main cases:

    1.   When the degree of the numerator is greater than or equal to the degree of the denominator, we first use polynomial long division to rewrite the function as a polynomial plus a proper fraction.

    2.  When the degree of the numerator is less than the degree of the denominator, the function is already a proper fraction, and we can apply the partial fraction decomposition method to integrate it.

  • Some Practical Examples on Partial Fractional Method File

    Try to read the solved example and solve the others.

  • Rationalizing Integrations File
  • Some Special Integrations File
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  Applications of Integrals

  • Areas and Volumes File