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MA25C01 APPLIED CALCULUS - Coggle Diagram
MA25C01 APPLIED CALCULUS
UNIT I DIFFERENTIAL CALCULUS
Limits at infinity
Derivative as a function
Continuity
Maxima and Minima of functions of single variable
Limit of a function
Mean Value theorem
New functions from old functions
Effect of derivatives on the shape of a graph
Graph of Functions
ACTIVITIES : Visualization of the functions, Maxima and Minima of functions using open source software , Solving of Competitive Examination questions(GATE)
Functions
UNIT II FUNCTIONS OF SEVERAL VARIABLES
Maxima ans minima of functions of two variables
Method of Lagrange’s multipliers
Total derivatives
Applications problems in engineering
Chain rule
ACTIVITIES : Partial Derivatives with two or three variables, Maxima and Minima of a function using open-source software, Solving of Competitive Examination questions(GATE)
Partial derivatives
UNIT III INTEGRAL CALCULUS
Arc Length
Area of Region
Improper Integrals
Indefinite integrals and Net Change theorem
Area of surface of revolution
Fundamental theorem of Calculus
ACTIVITIES : Definite and Indefinite Integrals, Determination of Area, Solving of Competitive Examination questions(GATE)
UNIT IV MULTIPLE INTEGRALS
Change of variables between Cartesian and polar co-ordinates
Evaluation of triple integrals
Change of order of integration
Change of variables between Cartesian and cylindrical and spherical co-ordinates
Evaluation of double integrals
ACTIVITIES : Double Integrals and triple integrals using open-source software, Solving of Competitive Examination questions(GATE)
Iterated integrals and Fubini’s theorem