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MTH301 - Calculus II
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Course Category: Mathematics
Course Level: Undergraduate
Credit Hours: 3
Pre-requisites: MTH101

Course Synopsis

This course focuses on two basic applications: Differential Calculus and Integral Calculus. Under these, we will study different techniques and some Fundamental theorems of calculus in multiple dimensions for example Stokes' theorem, Divergence theorem, Green's theorem, Other topics of discussion are Limits and Continuity, Extreme values, Fourier series and Laplace transformations.

Course Learning Outcomes

Upon successful completion of this course, you should be able to:
  • Determine Limits and Continuity of multi-variable function
  • Evaluate Partial Differentiation and will know the related techniques
  • Apply the concept of Extreme-Values of multi-variable functions to real world problems
  • Solve Double Integral for Cartesian and Polar co-ordinates and can do their inter-conversions
  • Find Triple Integrals in rectangular, spherical and cylindrical co-ordinates
  • Apply Multiple Integrals for area and volume problems
  • Apply elementary operations on Vector-Valued function
  • Compute arc-length and solve problems regarding change of parameter
  • Evaluate Line, Surface and Volume integral
  • State Green’s Theorem, Divergence Theorem and Stoke’s Theorem and show how these theorems are applied
  • Find Fourier Series of given periodic function
  • Solve problems related to Laplace Transformation

Course Contents

Introduction to three dimensional geometry. Limits, continuity and Partial Derivatives of Multivariable Function. Vectors. Directional derivative. Tangent Planes and Normal Lines to the Surfaces. Maxima And Minima of Functions of two variables. Applications of Extrema of Functions. Double Integration in rectangular and polar coordinates. Vector Valued Functions. Integration of Exact differentials. Line integrals. Greens Theorem and its application. Divergence and Curl of a vector. Scalar Fields, Vector fields, Volume and Surface integrals. Conservative Fields. Divergence Theorem. Fourier Series. Laplace Transforms.

Course Related Links

For basic rules of differentiation and their proofs
You can find useful material related to function of one variable on this site
You can find the topics related to integration, application of integration, geometry , curves and polar coordinates
Anitmated Description of topics
Online notes on Multivariable Calculus
A very valuable link containing online lectures being delivered by electronic pen
Course Instructor

Dr. M. Anwar Rao, Ph.D University of Manchester, UK


Calculus with Analytic Geometry by Howard Anton

Further Engineering Mathematics by K. A. Stroud