Professor: Leonardo Colò
Program: Honours Mathematics
Course code: MATH 138
Section: 081
Workload: Jan-Apr 2024 (12 weeks)
Delivery method Online

1. Integration (1 weeks):
   • - Areas under Curves.
     - Displacement versus Velocity.
     - Introduction to Riemann Sums.
     - Definition and properties of the Integral.
     - Geometric Interpretation of the Integral.
     - Average Value of a Function.
     - Differentiation of an Integral Function
     - Antiderivatives.
     - Fundamental Theorem of Calculus.
2. Techniques of Integration (2 weeks):
   • - Change of Variables.
     - Inverse Trigonometric Substitutions.
     - Integration by Parts.
     - Partial fractions.
3. Improper integrals (1 week):
   • - Introduction to Improper Integrals.
     - Monotone Convergence Theorem for Functions.
     - Comparison Test for Integrals.
     - The Gamma Function.
     - Type II Improper Integrals.
4. Applications of Integration (1 week):
   • - Areas Between Curves.
     - Volumes of Revolution: Disk Method.
     - Volumes of Revolution: Shell Method
     - Length of a Curve.
5. Differential Equations (2 weeks):
   • - Introduction to Differential Equations.
     - Graphical and Numerical Solutions of DEs.
     - Separable Differential Equations.
     - Linear Differential Equations.
     - Initial Value Problems
     - Examples: Exponential Growth, Newton's Law of Cooling and Logistic Growth.
6. Numerical Series (3 semaine):
   • - Introduction to Series and their properties.
     - Divergence Test.
     - Monotone Convergence Theorem.
     - Comparison Test.
     - Limit Comparison Test.
     - Integral Test.
     - Alternating Series.
     - Absolute vs Conditional Convergence
     - Ratio and Root Tests.
     
7. Power Series (2 weeks):
   • - Radius of Convergence.
     - Functions Represented by Power Series.
     - Building Power Series.
     - Differentiation and Integration of Power Series.
     - Taylor's Polynomials.
     - Introduction to Taylor Series.