Course Description: This course introduces computer application students to fundamental mathematical topics: differential equations, Laplace transforms, linear programming, and numerical methods.

Prerequisite: Derivatives, integrals.

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🎯 Course Outcomes (CO)

CO No.	Expected Outcome	Learning Domain
CO1	Understand Methods of solving Differential Equations: Separable ODEs, Exact ODEs, Integrating Factors, Linear ODEs.	Understand
CO2	Understand Laplace Transform, Linearity, first shifting theorem, Transforms of Derivatives and transform of integrals.	Apply
CO3	Understand the definition of Linear Programming Problems (LPP), differentiate between canonical and standard forms, and apply graphical and simplex methods for solution.	Understand
CO4	Apply numerical methods for solving algebraic and transcendental equations, including bisection, false position, Newton-Raphson, and numerical integration techniques like trapezoidal and Simpson's 1/3 rule.	Apply

🗺️ Mapping of Course Outcomes to PSOs

PSO 1	PSO 2	PSO 3	PSO 4	PSO 5	PSO 6	PSO 7
✓ (CO1)	✓ (CO1)	✓ (CO1)	✓ (CO1)	-	-	-
✓ (CO2)	✓ (CO2)	✓ (CO2)	-	-	-	-
✓ (CO4)	✓ (CO4)	✓ (CO4)	-	-	-	-
✓ (CO5)	✓ (CO5)	-	-	-	-	-

Module	Unit	Description	Hours
I	1	First Order ODEs: Basic Concepts, Modeling	13
	2	Separable ODEs
	3	Exact ODEs. Integrating Factors
	4	Linear ODEs
II	1	Laplace Transform, Linearity, First Shifting Theorem (s-Shifting)	14
	2	Transforms of Derivatives, transform of integrals, ODEs
		(Inverse Laplace & applications)
III	1	Linear Programming: Introduction	14
	2	Requirements of LPP
	3	Areas of application of LPP
	4	Graphical method of solution
	5	Canonical and standard form of LPP
	6	The simplex method (Technique and algorithm)
IV	Numerical Methods: Solution of algebraic and transcendental equations		14
	a) Introduction, b) Bisection Method, c) Newton Raphson method
	Numerical integration: a) Trapezoidal rule, b) Simpson's 1/3 rule
	(False position reference included)
	Applications & Error analysis
V	Teacher Specific Module: Formulation of LPP (Module III) & Advanced Numerical applications		5

Main Textbooks

• Advanced Engineering Mathematics (10th ed.), E. Kreyszig, Wiley, 2015
• Operations Research (Revised Ed.), Er. Prem Kumar Gupta & Dr. D.S. Hira
• Introductory Methods of Numerical Analysis (5th ed.), S.S. Sastry, PHI Learning

* Two written tests required. Average of best two considered for internal marks.
** Scientific calculators (up to fx-99) permitted.

✅ Daily lecture notes, video links, assignments, quizzes, and viva questions for Differential Equations · Laplace · LPP · Numerical Methods are available in this folder.

🔗 📖 Lecture Notes | 📝 Assignments | 🧪 Quizzes | 🎤 Viva