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Mathematical Analysis - BSc 4th Year Mathematics Full Course & Notes
in 4th Year
Created by
Hamromaster
About this course
Mathematical Analysis
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Multivariable differentiation
7 Parts
Day -60- Multivariable differentiation- directional derivative + partial derivative with example
363.49 MB
Day -61- Multivariable differentiation- example of directional derivative without continuity + total derivative
387.88 MB
Day -62- Multivariable differentiation- theorem on total derivative = directional derivative + derivative imply continuity
408.45 MB
Day-63- Multivariable differentiation- Jacobian matrix + chain rule introduction
443.98 MB
Day-64- Multivariable differentiation- Mean value theorem
411.78 MB
Day -65- Multivariable differentiation- Some important examples
376.42 MB
Day-66- Multivariable differentiation- Young's theorem
432.78 MB
Riemann-Stieltjes integrals
12 Parts
Day-48- Riemann-Stieltjes integrals- Introduction+linearity theorem
388.21 MB
Day-49- Riemann Stieltjes integral- Additive + integration by part theorem
390.33 MB
Day-50- Riemann Stieltjes integral- Relation between R-S integral and R integral
407.41 MB
Day-51- Riemann Steiltjes integral- Step function
342.02 MB
Day-52- Riemann Stieltjes integral- theorem on upper ,lower integral
370.25 MB
Day-53- Riemann Stieltjes integral- Theorem on equivalent condition between R-S integral
393.19 MB
Day-54- Riemann Stieltjes integral- Theorem on order preserving property
393.51 MB
Day-55- Riemann Stieltjes integral-theorem on integral of two functions
367.95 MB
Day-56- Riemann Stieltjes integral- First mean value theorem
390.31 MB
Day -57- Riemann Steiltjes integral- Important theorem on R-S integral
47.55 MB
Day -58- Riemann Stieltjes integral - First fundamental theorem of integral calculus
341.55 MB
Day-59- Riemann Stieltjes integral- Second fundamental theorem of integral calculus
397.63 MB
Limits and continuity
4 Parts
Day-44- Limits and continuity- Important theorem on cauchy sequence
388.29 MB
Day-45- Limits and continuity- Theorem on compact and sequentially compact set
426.43 MB
Day-46- Limits and continuity- Continuous function and it's theorem
434.46 MB
Day-47- Limits and continuity- Theorem on continuous function with closed sets
364.29 MB
Analytic functions
4 Parts
Day-40- Analytic functions- limit+ Continuity + differentiable of complex. valued function
402.35 MB
Day-41- Analytic function- Cauchy Reimann equation
384.36 MB
Day-42- Analytic functions- Some important theorem
371.42 MB
Day-43- Analytic function- Reflection principle
413.72 MB
Complex numbers
4 Parts
Day-36- Complex numbers- Introduction+ conjugate of complex number
421.39 MB
Day-37- Complex numbers and functions- Modulus of Complex number
378.11 MB
Day-38- Complex numbers
399.41 MB
Day-39- Complex numbers-Sketch the image under the transformation
400.17 MB
Euclidean space and metric space
11 Parts
Day-1- Euclidean space and metric space- introduction + discussion of syllabus
404.43 MB
Day-2- Euclidean space and metric space- Theorem on norms
380.08 MB
Day-3- Euclidean space and metric space- Cauchy schwarz inequality
372.9 MB
Day-4- Euclidean space and metric space- open ball,interior point,exterior point, open sets
408.33 MB
Day-5-Euclidean space and metric space- boundary point+ Theorem on union and intersection of open sets
369.67 MB
Day-6- Euclidean space and metric space- Closed sets+ Theorem on union, intersection of closed sets
412.48 MB
Day-7- Euclidean space and metric space- Adherent point, limit point and theorem on it
379.83 MB
Day-8- Euclidean space and metric space- Theorem relating closed set with adherent points + dense set
432.88 MB
Day-9- Euclidean space and metric space- Introduction of metric space and theorem on it
381.38 MB
Day-10- Euclidean space and metric space- prove of some important example of metric space
311.28 MB
Day-11- Metric space and Euclidean space- Theorem on subspace
388.16 MB
Compactness and covering properties
6 Parts
Day-12- Compactness and covering properties - general introduction + Leindelof covering theorem
424.12 MB
Day-13- Compactness and covering properties- Heine Borel theorem
373.44 MB
Day-14-Compactness and covering properties- compact set and its theorem
424.97 MB
Day-15- Compactness and covering properties- Theorem on compact sets
301.22 MB
Day-16- Compactness and covering properties - Theorem on compact sets continued
383.86 MB
Day -17- compactness and covering properties- Theorem on compact sets for metric space
336.24 MB
function of bounded variation
6 Parts
Day-18- function of bounded variation - Introduction+ Theorem to be of BV
405.28 MB
Day-19- functions of bounded variation- Theorem for a function to be bounded variation+ examples on it-
385.52 MB
Day-20- Functions of bounded variation- Examples on bounded variation+ introduction of total variation -
378.75 MB
Day-21- function of bounded variation- Bounded variation of sum,difference ,product and reciprocal .
393.43 MB
Day-22- Functions of bounded variation-Additive property ot total variation + total variation function
359.9 MB
Day-23- Functions of bounded variation- total variation functions and it's theorem.
454.05 MB
sequence and series of a function
6 Parts
Day-24- Sequence and series of a functions- introduction and solved example
376.95 MB
Day-25- Sequence and series of a functions- pointwise convergence+ uniform convergence-
413.52 MB
Day-26- Sequence and series of functions- Cauchy conditions for sequence+ Dini's uniform convergence theorem
433.96 MB
Day-27- Sequence and series of functions- Cauchy condition for series+ weierstrass M test
398.13 MB
Day-28- Sequence and series of test- Dirichlet test
386.36 MB
Day-29- Sequence and series of a function - Abel's theorem+ Continuity of limit function
396.29 MB
Improper Integral
6 Parts
Day-30- Improper integral- Introduction and it's type
400.76 MB
Day-31- Improper integral- Cauchy criterion + Direct comparison test
400.57 MB
Day-32- Improper integral- Limit comparison test
421.7 MB
Day-33- Improper integral- Absolutely convergence
382.29 MB
Day -34- Improper Integral- Dirichlet's test+ Abel's test for integral
361.62 MB
Day-35- Improper integral - Improper integral of second kind
371.01 MB
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