Differential Calculus and Integral Calculus (B.Sc Mathematics)

Limits, continuity, differentiability, expansions, curve tracing, definite integrals, Beta and Gamma functions and multiple integrals.

6 महीनेअवधि 6Chapters30टॉपिक

अभी पूछताछ करें

सिलेबस · पाठ्यक्रम

Download PDF

01Unit 1: Limits, Continuity and Differentiability 5 टॉपिक

Epsilon-delta definition of limit
Continuity and types of discontinuity
Differentiability
Successive differentiation
Leibnitz theorem

02Unit 2: Mean Value Theorems and Expansions 5 टॉपिक

Rolle's theorem
Lagrange's and Cauchy's mean value theorems
Taylor's and Maclaurin's theorems with remainders
Expansion of functions
Indeterminate forms and L'Hospital's rule

03Unit 3: Partial Differentiation and Curve Tracing 6 टॉपिक

Partial derivatives
Euler's theorem on homogeneous functions
Asymptotes
Curvature
Singular points
Tracing of Cartesian and polar curves

04Unit 4: Definite Integrals and Reduction Formulae 4 टॉपिक

Riemann integral and properties
Fundamental theorem of calculus
Reduction formulae for sin^n x and cos^n x
Wallis' formula

05Unit 5: Beta and Gamma Functions 5 टॉपिक

Definitions and convergence
Properties of Gamma function
Relation B(m, n) = Gamma(m) Gamma(n)/Gamma(m + n)
Duplication formula
Evaluation of integrals

06Unit 6: Multiple Integrals and Applications 5 टॉपिक

Double and triple integrals
Change of order of integration
Change of variables and Jacobian
Dirichlet's integral
Area, volume, rectification and volumes of revolution

परिचय

आप यह कर पाएँगे

Test limits, continuity and differentiability of real functions
Apply Leibnitz, Rolle, Lagrange and Taylor theorems and evaluate indeterminate forms
Use partial differentiation and Euler's theorem; find asymptotes and trace curves
Evaluate definite integrals with reduction formulae and Wallis' formula
Use Beta and Gamma functions to evaluate integrals
Evaluate double and triple integrals and find areas and volumes

यह किसके लिए है

B.Sc Mathematics students of Semester 1 (UP State Universities, NEP 2020)
First-year students starting the B.Sc Mathematics major

आपको क्या चाहिए

Class 12 Mathematics (calculus)

सवाल

Which syllabus does this subject follow?

It follows the B.Sc Mathematics Semester 1 syllabus of the UP State Universities (NEP 2020 common minimum syllabus). Where your own university's syllabus differs, the centre follows your university syllabus.

How are students assessed at the centre?

Through unit-wise multiple-choice tests, a final test paper and doubt-clearing sessions that follow the university examination pattern.

Will this help in the semester examination?

Yes. Units are taught in the university order with solved numericals and exam-pattern questions.