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Calculus II

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Calculus II

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Course Title: Calculus II

Course No: BDS154

Nature of the Course: THEORY

Semester: 2

Full Marks: 45 + 30

Pass Marks: 18 + 12

Credit Hours: 3

Course Description

Course Objectives

Course Contents

1. Parametric Equations and Polar Coordinates
8 hrs
1.1. Curves defined by parametric equations
1.2. Calculus with parametric curves
1.3. Polar coordinates
1.4. Areas and lengths in polar coordinates
1.5. Conic sections
1.6. Conic sections in polar coordinates
2. Infinite Sequences and Series
12 hrs
2.1. Sequences
2.2. Series
2.3. Comparison tests
2.4. Alternating series
2.5. Absolute convergence
2.6. Ratio test
2.7. Root test
2.8. Integral test and estimates of sums
2.9. Power series
2.10. Taylor and Maclaurin series
2.11. Taylor polynomials and their applications
3. Fourier Analysis
8 hrs
3.1. Fourier series
3.2. Periodic functions
3.3. Odd and even functions
3.4. Fourier series for arbitrary range
3.5. Half range Fourier series
3.6. Fourier integral theorem
3.7. Fourier sine and cosine integral
3.8. Complex form of Fourier integral
3.9. Fourier transform
3.10. Fourier sine transform
3.11. Fourier cosine transform and their properties
4. Partial Derivatives
11 hrs
4.1. Functions of two and three variables
4.2. Limits and continuity
4.3. Partial derivatives
4.4. Higher order partial derivatives
4.5. Tangent planes and linear approximations
4.6. Directional derivatives and gradient vector
4.7. Total differentials
4.8. Euler’s theorem of two and three variables
4.9. Maximum and minimum values
4.10. Lagrange multipliers
5. Multiple Integrals
9 hrs
5.1. Double integrals over rectangle
5.2. Iterated integrals
5.3. Double integrals over general regions
5.4. Double integrals in polar coordinates
5.5. Applications of double integrals
5.6. Triple integrals
5.7. Change of variables in multiple integral

Reference Books

  1. 1.Stewart J., Calculus: Early Transcendental Functions, 7th edition, Thomson Brooks/Cole.
  2. 2.Larson, et al, Calculus: Early Transcendental Functions, Houghton Mifflin, 2011.
  3. 3.Robert A. Adams, Christopher Essex, Calculus: a complete course, Pearson, 2010.
  4. 4.Kreyszig, E., Advance Engineering Mathematic, Tenth edition, Wiley, New York.

Notes:

Source:

This course is a continuation in Calculus I. It covers parametric equations and polar coordinates, infinite sequences and series, Fourier analysis. It also focuses on the comprehensive treatment of partial derivatives, optimization problems and multiple integrals.

After successful completion of this course the student will be able to

  • solve problems of infinite sequences and series
  • obtain the elementary knowledge of Fourier series and Fourier transform
  • to calculate derivatives of multivariable functions
  • to solve the problems of double and triple integrals
  • apply the techniques of calculus to solve real life problems.
This syllabus follows the official BDS curriculum of Tribhuvan University. In case of any doubt or revision, the university's published syllabus shall be considered authoritative.