| Notes | |
|---|---|
| MA25C01 - Applied Calculus | MA25C01 Notes Collection 1 |
| Question Bank | |
|---|---|
| MA25C01 - Applied Calculus | MA25C01 Question Bank Collection 1 |
| Previous Year Question paper | |
|---|---|
| MA25C01 - Applied Calculus | MA25C01 PYQ Collection 1 |
Syllabus
MA25C01 Applied Calculus
Course Objectives:
- To provide technical competence of modelling engineering problems using calculus.
- To apply the calculus concepts in solving engineering problems using analytical methods and computational tools.
Unit - 1
Differential Calculus: Functions, graph of functions, New functions from old functions,
Limit of a function, Continuity, Limits at infinity, Derivative as a function, Maxima and
Minima of functions of single variable, Mean value theorem, Effect of derivatives on the
shape of a graph.
Activities: Visualization of the functions, Maxima and Minima of a function using opensource software, Solving of Competitive Examination questions (Ex. GATE).
Unit - 2
Functions of Several Variables: Partial derivatives, Chain rule, Total derivative,
Maxima and minima of functions of two variables, Method of Lagrange’s Multipliers,
Application problems in engineering.
Activities: Partial Derivatives with two or three variables, Maxima and Minima of a
function using open-source software, Solving of Competitive Examination questions (Ex.
GATE).
Unit - 3
Integral Calculus: Fundamental theorem of Calculus, Indefinite integrals and the Net
Change Theorem, Improper integrals, Arc Length, Area of Region, Area of surface of
revolution.
Activities: Definite and Indefinite Integrals, Determination of Area, Solving of
Competitive Examination questions (Ex. GATE).
Unit -4
Multiple Integrals: Iterated integrals and Fubini’s theorem, Evaluation of double
integrals, change of order of integration, change of variables between Cartesian and
polar co-ordinates, evaluation of triple integrals-change of variables between Cartesian
and cylindrical and spherical co-ordinates.
Activities: Double integrals and triple integrals using open-source software, Solving of
Competitive Examination questions (Ex. GATE).
Weightage: Continuous Assessment: 40%, End Semester Examinations: 60%.
Assessment Methodology: Assignments (20%), Solution to application-oriented
problems using software (20%), Solving of GATE questions (20%), Internal
Examinations (40%).
References:
1. Anton, H., Bivens, I. C., & Davis, S. (2021). Calculus: Early transcendentals. John
Wiley & Sons.
2. Ron Larson and David C. Falvo, (2013), Calculus: an Applied Approach. Cengage
Learning.
3. Stewart, J., Clegg, D., & Watson, S. (2019). Calculus: Early transcendentals.
4. Thomas, G. B., Jr., Weir, M. D., Hass, J., & Heil, C. (2018). Thomas' calculus: Early
transcendentals. Pearson.
5. Singh, K. (2019). Engineering mathematics through applications. Bloomsbury
Publishing.
6. Grewal, B. S. (2012). Higher engineering mathematics. Khanna Publishers.
E-resources:
1. https://math.libretexts.org/Bookshelves/Calculus/Map%3A_Calculus__Early_Trans
cendentals_(Stewart)/
2. https://openstax.org/books/calculus-volume-1/
3. https://tutorial.math.lamar.edu/Classes/CalcII/CalcII.aspx
4. SCILAB, https://www.scilab.org/
