Calculus II#

This course emphasizes intuitive and conceptual understanding of multivariable calculus, alongside essential computational skills. Topics include infinite and Fourier series, vector-valued functions, partial derivatives, multiple integrals, and line and surface integrals. The course also cultivates the ability to apply calculus to problems in the sciences and engineering.

Upon completing this course, students are expected to master the fundamental concepts, theories, and operations of multivariable calculus, particularly the basic ideas of differentiation and integration, and the computation of various integrals. They will also be able to solve basic ordinary differential equations, determine the convergence or divergence of infinite series, and represent functions using power series. This course aims to help students develop skills in abstract thinking, logical reasoning, and mathematical analysis, encouraging them to focus on mathematical methods and acquire certain computational abilities. They will be able to use their knowledge to analyze and solve practical problems in the future.

Specific learning outcomes include:

  • Understand the concept of infinite series, master the rules for determining the convergence or divergence of infinite series, and be able to expand functions into power series.
  • Understand Vectors and the Geometry of Space, be able to compute the equations of lines and planes in space, and be familiar with cylinders and quadric surfaces.
  • Understand vector fields and be able to use them to calculate the curvature and normal vectors of curves in space, as well as the tangential and normal components of acceleration.
  • Understand partial derivatives and various rules for calculating them, and be able to apply partial derivatives to practical problems in geometry and optimization.
  • Understand the basic ideas of multiple integrals, be able to compute multiple integrals in different coordinate systems, and apply them to simple practical problems in physics.
  • Understand and be able to compute line integrals and surface integrals, and be familiar with Green’s theorem, Stokes’ theorem, and the divergence theorem.
  • Able to solve second-order linear constant coefficient ordinary differential equations.

Textbook:#

Thomas’ Calculus: Early Transcendentals, 15th edition, Published by Pearson

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