Vysakh: deduplicated

2025-07-28T19:36:07Z

deduplicated

← Older revision		Revision as of 19:36, 28 July 2025
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	~~=== MA1001E MATHEMATICS I ===~~
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	~~! L !! T !! P !! O !! C~~
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	~~Total Lecture Sessions: 39~~
	~~==== Course Outcomes: ====~~
	* CO1: Formulate some engineering problems as ODEs and hence solve such problems.
	* CO2: Solve linear ODEs with constant coefficients.
	* CO3: Find the limits, check for continuity and differentiability of real valued functions of two variables.
	* CO4: Test for the convergence of sequences and series.
	* CO5: Find the Fourier series representing periodic functions.

	~~==== Course Content: ====~~
	~~===== Ordinary Differential Equations =====~~
	* Existence and uniqueness of solution of first order ODE
	* Methods of solutions of first order ODE
	* Linear ODE
	* Orthogonal Trajectories
	* Linear homogeneous second order ODEs with constant coefficients
	* Fundamental system of solutions
	* Existence and uniqueness of solutions
	* Wronskian
	* Method of undetermined coefficients
	* Solution by variation of parameters
	* Euler-Cauchy equations
	* Applications of first and second order ODEs
	* System of linear ODEs with constant coefficients

	~~===== Functions of Several Variables =====~~
	* Limit, Continuity
	* Partial derivatives, Partial differentiation of composite functions
	* Directional derivatives, Gradient
	* Local maxima and local minima of functions of two variables
	* Critical point, Saddle point
	* Taylor’s formula for two variables, Hessian, Second derivative test
	* Method of Lagrange multipliers
	* Parameterised curves in space, Arc length, Tangent and normal vectors, Curvature and torsion

	~~===== Sequences, Series, and Fourier Analysis =====~~
	* Sequences, Cauchy sequence, Convergence of sequences
	* Series, Convergence of series, Tests for convergence, Absolute convergence
	* Sequence of functions, Power series, Radius of convergence, Taylor series
	* Periodic functions and Fourier series expansions, Half-range expansions
	* Fourier integral, Fourier transforms and their properties

	=== MA1001E MATHEMATICS I ===		=== MA1001E MATHEMATICS I ===
	{\| class="wikitable"		{\| class="wikitable"

Vysakh: added more links and init. fyi links don't work.

2025-07-28T19:35:03Z

added more links and init. fyi links don't work.

New page

=== MA1001E MATHEMATICS I ===
{| class="wikitable"
|-
! L !! T !! P !! O !! C
|-
| 3 || 1* || 0 || 5 || 3
|}
Total Lecture Sessions: 39
==== Course Outcomes: ====
* CO1: Formulate some engineering problems as ODEs and hence solve such problems.
* CO2: Solve linear ODEs with constant coefficients.
* CO3: Find the limits, check for continuity and differentiability of real valued functions of two variables.
* CO4: Test for the convergence of sequences and series.
* CO5: Find the Fourier series representing periodic functions.

==== Course Content: ====
===== Ordinary Differential Equations =====
* Existence and uniqueness of solution of first order ODE
* Methods of solutions of first order ODE
* Linear ODE
* Orthogonal Trajectories
* Linear homogeneous second order ODEs with constant coefficients
* Fundamental system of solutions
* Existence and uniqueness of solutions
* Wronskian
* Method of undetermined coefficients
* Solution by variation of parameters
* Euler-Cauchy equations
* Applications of first and second order ODEs
* System of linear ODEs with constant coefficients

===== Functions of Several Variables =====
* Limit, Continuity
* Partial derivatives, Partial differentiation of composite functions
* Directional derivatives, Gradient
* Local maxima and local minima of functions of two variables
* Critical point, Saddle point
* Taylor’s formula for two variables, Hessian, Second derivative test
* Method of Lagrange multipliers
* Parameterised curves in space, Arc length, Tangent and normal vectors, Curvature and torsion

===== Sequences, Series, and Fourier Analysis =====
* Sequences, Cauchy sequence, Convergence of sequences
* Series, Convergence of series, Tests for convergence, Absolute convergence
* Sequence of functions, Power series, Radius of convergence, Taylor series
* Periodic functions and Fourier series expansions, Half-range expansions
* Fourier integral, Fourier transforms and their properties

=== MA1001E MATHEMATICS I ===
{| class="wikitable"
|-
! L !! T !! P !! O !! C
|-
| 3 || 1* || 0 || 5 || 3
|}
Total Lecture Sessions: 39
==== Course Outcomes: ====
* CO1: Formulate some engineering problems as ODEs and hence solve such problems.
* CO2: Solve linear ODEs with constant coefficients.
* CO3: Find the limits, check for continuity and differentiability of real valued functions of two variables.
* CO4: Test for the convergence of sequences and series.
* CO5: Find the Fourier series representing periodic functions.

==== Course Content: ====
===== Ordinary Differential Equations =====
* Existence and uniqueness of solution of first order ODE
* Methods of solutions of first order ODE
* Linear ODE
* Orthogonal Trajectories
* Linear homogeneous second order ODEs with constant coefficients
* Fundamental system of solutions
* Existence and uniqueness of solutions
* Wronskian
* Method of undetermined coefficients
* Solution by variation of parameters
* Euler-Cauchy equations
* Applications of first and second order ODEs
* System of linear ODEs with constant coefficients

===== Functions of Several Variables =====
* Limit, Continuity
* Partial derivatives, Partial differentiation of composite functions
* Directional derivatives, Gradient
* Local maxima and local minima of functions of two variables
* Critical point, Saddle point
* Taylor’s formula for two variables, Hessian, Second derivative test
* Method of Lagrange multipliers
* Parameterised curves in space, Arc length, Tangent and normal vectors, Curvature and torsion

===== Sequences, Series, and Fourier Analysis =====
* Sequences, Cauchy sequence, Convergence of sequences
* Series, Convergence of series, Tests for convergence, Absolute convergence
* Sequence of functions, Power series, Radius of convergence, Taylor series
* Periodic functions and Fourier series expansions, Half-range expansions
* Fourier integral, Fourier transforms and their properties

==== References: ====
* 1. Anton, H., Bivens, I., & Davis, S. (2015). *Calculus*, 10th Ed. New York: John Wiley & Sons. [https://www.wiley.com/en-us/Calculus%2C+10th+Edition-p-9781118671720]
* 2. Thomas, G. B., Weir, M. D., & Hass, J. (2015). *Thomas' Calculus*, 12th Ed. New Delhi, India: Pearson Education. [https://www.pearson.com/us/higher-education/product/Thomas-Thomas-Calculus-12th-Edition/9780321878952.html]
* 3. Kreyszig, E. (2015). *Advanced Engineering Mathematics*, 10th Ed. New York: John Wiley & Sons. [https://www.wiley.com/en-us/Advanced+Engineering+Mathematics%2C+10th+Edition-p-9780470458365]
* 4. Apostol, T. M. (2014). *Calculus, Vol. 1: One-Variable Calculus with an Introduction to Linear Algebra*, 1st Ed. New Delhi: Wiley. [https://www.amazon.in/Calculus-Vol-One-Variable-Introduction-Algebra/dp/8126553857]

Mathematics I - Revision history

Vysakh: deduplicated

Vysakh: added more links and init. fyi links don't work.