# Applied Mathematics for MSBTE K Scheme (II - Common - 312301)

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Syllabus Applied Mathematics - (312301) Learning Scheme Credits Assessment Scheme Actual Contact Hrs./Week SLH NLH Paper Duration Theory Based on LL & TL Based on SL Total Marks CL TL LL Practical FA-TH SA-TH Total FA-PR SA-PR SLA Max Max Max Min Max Min Max Min Max Min 3 1 - - 4 2 3 30 70 100 40 - - - - - - 100 Sr. No. Theory Learning Outcomes(TLO's) aligned to CO's. Learning content mapped with Theory Learning Outcomes (TLO's) and CO's. 1. TLO 1.1 Solve the given simple problem(s) based on rules of integration. TLO 1.2 Evaluate the given simple integral(s) using substitution method. TLO 1.3 Integrate given simple functions using the integration by parts. TLO 1.4 Solve the given simple integral by partial fractions. Unit - I Indefinite Integration 1.1 Simple Integration : Rules of integration and integration of standard functions. 1.2 Integration by substitution. 1.3 Integration by parts. 1.4 Integration by partial fractions. (only linear non repeated factors at denominator of proper fraction). (Chapter - 1) 2. TLO 2.1 Solve given examples based on definite Integration. TLO 2.2 Use properties of definite integration to solve given problems. Unit - II Definite Integration 2.1 Definite Integration : Definition, rules of definite integration with simple examples. 2.2 Properties of definite integral (without proof) and simple examples. (Chapters - 2, 3) 3. TLO 3.1 Find the order and degree of given differential equations. TLO 3.2 Form simple differential equation for given elementary engineering problems. TLO 3.3 Solve given differential equations using the methods of Variable separable and Exact Differential Equation (Introduce the concept of partial differential equation). TLO 3.4 Solve given Linear Differential Equation. Unit - III Differential Equation 3.1 Concept of Differential Equation. 3.2 Order, degree and formation of Differential equations. 3.3 Methods of solving differential equations : Variable separable form, Exact Differential Equation, Linear Differential Equation. (Chapters - 4, 5) 4. TLO 4.1 Find roots of algebraic equations by using appropriate methods. TLO 4.2 Solve the system of equations in three unknowns by iterative methods. TLO 4.3 Solve problems using Bakhshali iterative methods for finding approximate square root. (IKS) Unit - IV Numerical Methods 4.1 Solution of algebraic equations : Bisection method, Regula Falsi method and Newton - Raphson method. 4.2 Solution of simultaneous equations containing three Unknowns by Iterative method : Gauss Seidal and Jacobi’s method. 4.3 Bakhshali iterative methods for finding approximate square root.(IKS) (Chapters - 6, 7) 5. TLO 5.1 Solve given problems based on repeated trials using Binomial distribution. TLO 5.2 Solve given problems when number of trials are large and probability is very small. TLO 5.3 Utilize the concept of normal distribution to solve related engineering problems. Unit - V Probability Distribution 5.1 Binomial distribution. 5.2 Poisson’s distribution. 5.3 Normal distribution. (Chapter - 8)

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