In this course, we will continue our journey in Calculus and turn our attention to the theory of integration (à la Riemann). We shall begin with the definition and techniques of integration, derive the Fundamental Theorem of Calculus that provides an important link between integration & differentiation, compute areas and volumes of some 2D/3D objects, discuss applications to analytic (plane) geometry and solve certain first order differential equations.

Definitions are discussed and the most important theorems are derived in the lectures with a view to help students to develop their abilities in logical deduction and analysis. Practical applications of Calculus in various fields are illustrated in order to promote a more organic interaction between the theory of Calculus and students' own fields of study. This course also provides TA classes in which students are able to make their skills in handling calculations in Calculus more proficient under the guidance of our teaching assistants.

If you wish to contact the instructor (Dr. Kwok-Wing Tsoi), please email to kwokwingtsoi@ntu.edu.tw

Provisional Schedule :

Week 9 - Integration àla Riemann and FTC
Week 10 - Technique 1 : Method of substitution
Week 11 - Technique 2 : Integration by parts, Integrating rational functions
Week 12 - Improper integrals and Laplace transform of special functions
Week 13 - Differential equations I : separable, linear
Week 14 - Differential equations II : second order ODEs
Week 15 - Reviews
Week 16 - Solving differential equations by Laplace transform (non-examinable)