46.45 GB | 00:42:36 | mp4 | 1280X720  | 16:9
Genre:eLearning |Language:English

Files Included :
1 -Introduction to the course  (138.18 MB)
2 -Two types of integrals, two ways to go  (110.38 MB)
3 -My choices versus the choices in the book  (142.56 MB)
4 -The spoiler you need to follow both paths  (217.81 MB)
5 -Main integration techniques and where to find them  (94.11 MB)
6 -Plenty of applications  (52.52 MB)
1 -Finding values of some integrals with help of geometry  (128.42 MB)
2 -Integrals of odd functions over compact and symmetric-to-zero intervals  (55.34 MB)
3 -Integrals of even functions over compact and symmetric-to-zero intervals  (76.74 MB)
4 -Integrals of periodic functions  (46.34 MB)
5 -Some nice properties of the mean value  (281.8 MB)
6 -Optional What about integrals equal to zero  (121.78 MB)
1 -The connection between finding areas and finding antiderivatives  (104.43 MB)
10 -Computing average values of functions on intervals, an example  (317.98 MB)
11 -Integration by parts for Riemann integrals, two ways to go  (183.99 MB)
12 -Integration by substitution for Riemann integrals, two ways to go  (346.25 MB)
13 -An illustration for integration by substitution  (113.53 MB)
14 -Applications of properties of integrals, an exercise  (405.34 MB)
15 -Limits of some type of sequences, Example 1  (279.46 MB)
16 -Limits of some type of sequences, Example 2  (201.4 MB)
17 -Limits of some type of sequences, Example 3  (140.04 MB)
18 -Limits of some type of sequences, Example 4  (135.33 MB)
19 -Limits of some type of sequences, Example 5  (239.93 MB)
2 -Algebraic and transcendental functions  (53.74 MB)
20 -Differentiating functions defined with help of integrals, Example 1  (102.98 MB)
21 -Differentiating functions defined with help of integrals, Example 2  (334.91 MB)
22 -Future Fundamental Theorems in Multivariable Calculus  (61.36 MB)
3 -What came first the logarithm or the exponential  (157.86 MB)
4 -Function of the upper limit of integration its continuity  (146.36 MB)
5 -Fundamental Theorem of Calculus, part 1  (136.67 MB)
6 -Fundamental Theorem of Calculus, part 2 (the evaluation theorem)  (96.96 MB)
7 -Area of a disc; another method for computing integrals from V147, V151, and V155  (451.44 MB)
8 -Evaluating integrals, another example  (294.55 MB)
9 -Important integrals for future applications (Fourier series)  (338.75 MB)
1 -Area between the graph of a function and the x-axis  (99.05 MB)
2 -Another (than in V36, V108, V114) method for finding antiderivative of secant  (408.09 MB)
3 -Area between two graphs  (247.46 MB)
1 -Arc length derivation of the formula, some examples  (277.48 MB)
2 -Arc length, Problem 1  (459.26 MB)
3 -Arc length, Problem 2  (195.16 MB)
1 -Rotational volume, different situations and different methods  (97.39 MB)
2 -The disk method derivation and an example  (74.74 MB)
3 -We are finally able to confirm two well-known formulas for volume  (226.69 MB)
4 -The washer method derivation and an example  (77.21 MB)
5 -Cylindrical shells derivation and an example  (111.77 MB)
6 -Cylindrical shells for a domain between two graphs  (53.47 MB)
1 -Rotational surface area derivation and two examples  (291.17 MB)
2 -Rotational surface area, Problem 1  (357.49 MB)
3 -Rotational surface area, Problem 2  (266.59 MB)
1 -Improper integrals, an introduction  (211.8 MB)
2 -Improper integrals of the first kind, Problem 1  (177.59 MB)
3 -Improper integrals of the first kind, Problem 2  (282.28 MB)
1 -Improper integrals of the second kind  (213.4 MB)
2 -Improper integrals of the second kind, Problem 1  (179.95 MB)
3 -Improper integrals of the second kind, Problem 2  (351.05 MB)
1 -Comparison criteria for improper integrals of non-negative functions  (494.3 MB)
2 -Comparison criteria, Problem 1  (182.87 MB)
3 -Comparison criteria, Problem 2  (376.36 MB)
4 -Wrap-up and some words about Calculus 2, part 2 Sequences and series  (34.94 MB)
1 -Bonus Lecture  (40.71 MB)
1 -Reverting differentiation in simple cases  (75.06 MB)
10 -Linearity of integration, Exercise 6  (154.03 MB)
11 -Linearity of integration, Exercise 7  (51.31 MB)
12 -Linearity of integration, Exercise 8  (139.53 MB)
13 -Linearity of integration, Exercise 9  (150.64 MB)
14 -Linearity of integration, Exercise 10  (101.11 MB)
15 -Linearity of integration, Exercise 11  (102.81 MB)
16 -Linearity of integration, Exercise 12  (212.9 MB)
17 -Linearity of integration, Exercise 13  (86.69 MB)
18 -Linearity of integration, Exercise 14  (155.77 MB)
19 -Linearity of integration, Exercise 15  (71.92 MB)
2 -Some important facts about primitive functions  (51.09 MB)
20 -A soft introduction to variable substitution  (95.47 MB)
21 -Easy variable substitution, Exercise 16  (155.69 MB)
22 -Easy variable substitution, Exercise 17  (144.52 MB)
23 -Easy variable substitution, Exercise 18  (135.99 MB)
24 -Easy variable substitution and some uneasy trigonometry, Problem 1  (97.8 MB)
25 -Easy variable substitution and some uneasy trigonometry, Problem 2  (210.03 MB)
26 -Easy variable substitution, Exercise 19  (217.86 MB)
27 -Easy variable substitution, Exercise 20  (118.96 MB)
28 -Logarithmic derivative and its charm  (22.9 MB)
29 -Logarithmic derivative, Exercise 21  (89.5 MB)
3 -Integrals of hyperbolic functions and some related stuff  (50.73 MB)
30 -Logarithmic derivative three difficult and important examples, Problem 3  (278.17 MB)
31 -The last one, Exercise 22  (97.62 MB)
4 -Linearity of integration  (54.59 MB)
5 -Linearity of integration, Exercise 1  (152.59 MB)
6 -Linearity of integration, Exercise 2  (168.11 MB)
7 -Linearity of integration, Exercise 3  (185.82 MB)
8 -Linearity of integration, Exercise 4  (170.52 MB)
9 -Linearity of integration, Exercise 5  (147.58 MB)
1 -Integration by parts how it works and when to use it  (77.92 MB)
10 -Integration by parts, Exercise 1  (183.36 MB)
11 -Integration by parts, Exercise 2  (239.56 MB)
12 -Integration by parts, Exercise 3  (107.51 MB)
13 -Integration by parts, Exercise 4  (216.72 MB)
14 -Integration by parts, Exercise 5  (116.65 MB)
15 -Integration by parts, Exercise 6  (495.38 MB)
2 -Integration by parts Example 1  (148.98 MB)
3 -Integration by parts Example 2  (109.17 MB)
4 -Integration by parts Example 3  (82.07 MB)
5 -Integration by parts Example 4  (287.77 MB)
6 -Integration by parts Example 5  (130.51 MB)
7 -Integration by parts Example 6  (106.88 MB)
8 -Integration by parts Example 7  (151.6 MB)
9 -What happens when the degree of the polynomial is higher  (48.02 MB)
1 -Integration by substitution how it works and when to use it, Example 1  (155.5 MB)
10 -Recognising (almost) derivatives, Example 10  (54.78 MB)
11 -Recognising (almost) derivatives, Example 11  (111.87 MB)
12 -Recognising (almost) derivatives, Example 12  (60.85 MB)
13 -Recognising (almost) derivatives, Example 13  (111.66 MB)
14 -Back to the integral from V49 for n=-1, Example 14  (60.24 MB)
15 -Back to the integral from V30, Problem 1  (208.3 MB)
16 -Different results can happen how to handle them, Problem 2  (64.98 MB)
17 -Optional Back to the integral of cosecant from V36, Problem 3  (343.34 MB)
18 -A less obvious case, Problem 4  (80.53 MB)
19 -A less obvious case, Problem 5  (128.92 MB)
2 -Easy substitutions from Section 2, Example 2  (325.11 MB)
20 -Three examples related to the arctangent, Problem 6  (247.48 MB)
21 -Back to arcsine, Problem 7  (212.92 MB)
22 -A strange one, Problem 8  (204.51 MB)
23 -Three examples with the square root of x  (150.38 MB)
3 -Recognising (almost) derivatives, Example 3  (164.19 MB)
4 -Recognising (almost) derivatives, Example 4  (75.4 MB)
5 -Recognising (almost) derivatives, Example 5  (87.45 MB)
6 -Recognising (almost) derivatives, Example 6  (42.74 MB)
7 -Recognising (almost) derivatives, Example 7  (86.86 MB)
8 -Recognising (almost) derivatives, Example 8  (98.4 MB)
9 -Recognising (almost) derivatives, Example 9  (59.94 MB)
1 -Five key concepts needed for the integration of rational functions  (51.7 MB)
10 -Variable substitution, logarithm, and arctangent, Formula 6  (372.5 MB)
11 -Method of Strategic Substitution in partial fraction decomposition  (350.35 MB)
12 -Integration of rational functions, Exercise 1  (389.75 MB)
13 -Integration of rational functions, Exercise 2  (150.86 MB)
14 -Integration of rational functions, Exercise 3  (387.66 MB)
15 -Integration of rational functions, Exercise 4  (288.57 MB)
16 -Integration of rational functions, Exercise 5  (256.03 MB)
17 -Integration of rational functions, Problem 1  (428.09 MB)
18 -Integration of rational functions, Problem 2  (581.34 MB)
19 -Integration of rational functions, Problem 3  (154.77 MB)
2 -Prerequisites from Precalculus 2  (287.92 MB)
20 -Integration of rational functions, Problem 4  (180.43 MB)
3 -We have already worked with integrals of rational functions  (138.01 MB)
4 -Integrals leading to the logarithm or to power functions, Formula 1  (193.72 MB)
5 -Integrals leading to the logarithm or to power functions, Formula 2  (282.97 MB)
6 -Integrals leading to the arctangent or to power functions, Formula 3  (273.17 MB)
7 -Formula 3, Example 3  (158.98 MB)
8 -Variable substitution and arctangent, Formula 4  (54.83 MB)
9 -Variable substitution and arctangent, Formula 5  (45.95 MB)
1 -Trigonometric formulas and where to find them  (49 MB)
10 -The product of powers of the sine and the cosine  (60.37 MB)
11 -The product of powers of the sine and the cosine, Exercise 3  (75.73 MB)
12 -The product of powers of the sine and the cosine, Exercise 4  (98.27 MB)
13 -Integrals involving secants and tangents, Exercise 5  (337.5 MB)
14 -Recursive formulas for integrals of powers of the tangent or of the secant  (127.93 MB)
15 -Product to sum formulas are good for integrals  (40.76 MB)
16 -Rational expressions in two variables  (132.23 MB)
17 -World's sneakiest substitution the universal substitution  (312.91 MB)
18 -The universal substitution, Exercise 6  (93 MB)
19 -The universal substitution, Exercise 7  (213.37 MB)
2 -Trigonometric integrals we have seen until now  (102.34 MB)
20 -The universal substitution, Exercise 8  (152.14 MB)
21 -The universal substitution, Exercise 9  (321.41 MB)
22 -Rational expressions odd w r t  the sine, Exercise 10  (312.64 MB)
23 -Rational expressions odd w r t  the sine, Exercise 11  (248.65 MB)
24 -Rational expressions odd w r t  the sine, Exercise 12  (186.73 MB)
25 -Rational expressions odd w r t  the cosine, Exercise 13  (256.95 MB)
26 -Rational expressions even w r t  both variables, Exercise 14  (693.73 MB)
27 -Rational expressions even w r t  both variables, Exercise 15  (403.02 MB)
28 -The last one, just for fun, Problem 1  (129.97 MB)
3 -Power reduction formulas for computing integrals of the sine (or cosine) squared  (29.39 MB)
4 -Integral of the cube of the sine or of the cosine, by change of variables  (250.9 MB)
5 -Integral of the fourth power of the sine with help of repeated power reduction  (75.78 MB)
6 -Recursive formulas for integrals of powers of the sine or of the cosine  (360.56 MB)
7 -Powers of the sine or of the cosine versus the functions of multiple arguments  (82.18 MB)
8 -Cubes in two ways, Exercise 1  (131.16 MB)
9 -Fourth powers in two ways, Exercise 2  (202.25 MB)
1 -Nobody will teach you all the integration techniques, but  (76.21 MB)
10 -Optional A geometrical interpretation of Euler's substitutions 2 and 3  (106.26 MB)
11 -Euler substitutions, Problem 1  (338.37 MB)
12 -Euler substitutions, Problem 2  (360.17 MB)
13 -Euler substitutions, Problem 3  (379.62 MB)
14 -Rational expressions of rational powers  (50.94 MB)
15 -Rational expressions of rational powers, Problem 4  (354.11 MB)
16 -Rational expressions of rational powers, Problem 5  (85.88 MB)
17 -Rational expressions of rational powers, Problem 6  (80.19 MB)
18 -Rational expressions of rational powers, Problem 7  (206.69 MB)
19 -Rational expressions of rational powers, an atypical one, Problem 8  (271.62 MB)
2 -Euler substitutions, why three cases are enough  (91.68 MB)
20 -Direct (u) versus inverse substitution  (82.63 MB)
21 -Back to trigonometric substitutions from Section 6 reference triangles  (129.67 MB)
22 -Three triangle substitutions  (59.91 MB)
23 -Triangle substitutions, Case 1  (84.74 MB)
24 -Triangle substitution 1, an example  (223.26 MB)
25 -Triangle substitution 1, Problem 9  (159.05 MB)
26 -Triangle substitution 1, Problem 10  (142.55 MB)
27 -Triangle substitutions, Case 2  (51.95 MB)
28 -Triangle substitution 2, an example  (209.04 MB)
29 -Triangle substitution 2, Problem 11  (213.51 MB)
3 -Euler substitutions, why they work  (42.91 MB)
30 -Triangle substitution 2, Problem 12  (131.39 MB)
31 -Triangle substitutions, Case 3  (57.73 MB)
32 -Triangle substitution 3, an example  (278.1 MB)
33 -Triangle substitution 3, Problem 13  (184.58 MB)
34 -Undetermined coefficients  (100.9 MB)
35 -Some remarks about equality of certain functions  (176.72 MB)
36 -Undetermined coefficients instead of integration by parts, an example  (228.21 MB)
37 -Undetermined coefficients instead of integration by parts, another example  (515.5 MB)
38 -Optional Our most complicated method  (62.1 MB)
39 -Optional Our most complicated method, an example  (482.86 MB)
4 -Euler's substitution 1, an explanation  (114.48 MB)
40 -Optional Our most complicated method, Problem 14  (430.85 MB)
5 -Euler's substitution 1, an example  (493.98 MB)
6 -Euler's substitution 2, an explanation  (74.21 MB)
7 -Euler's substitution 2, an example  (365.38 MB)
8 -Euler's substitution 3, an explanation  (46.33 MB)
9 -Euler's substitution 3, an example  (348.19 MB)
1 -Practice, practice, practice  (57.39 MB)
10 -Integrals, Problem 9  (139.49 MB)
11 -Integrals, Problem 10  (215.12 MB)
12 -Integrals, Problem 11  (259 MB)
13 -Integrals, Problem 12  (203.25 MB)
14 -Integrals, Problem 13  (103.61 MB)
15 -Integrals, Problem 14  (129.67 MB)
16 -Integrals, Problem 15  (74.9 MB)
17 -Integrals, Problem 16  (294.55 MB)
18 -Integrals, Problem 17  (360.21 MB)
19 -A very brief introduction to Initial-Value Problems (IVP)  (124.49 MB)
2 -Integrals, Problem 1  (198.2 MB)
20 -IVP verifying solutions, an example  (154.13 MB)
21 -IVP finding solutions, an example  (101.57 MB)
22 -Position, velocity, acceleration  (102.37 MB)
23 -Position, velocity, acceleration, Problem 18  (310.94 MB)
24 -IVP Falling under gravity, Problem 19  (283.92 MB)
25 -Direct versus inverse problems  (51.15 MB)
3 -Integrals, Problem 2  (257.61 MB)
4 -Integrals, Problem 3  (149.43 MB)
5 -Integrals, Problem 4  (103.37 MB)
6 -Integrals, Problem 5  (120.98 MB)
7 -Integrals, Problem 6  (142.59 MB)
8 -Integrals, Problem 7  (164.09 MB)
9 -Integrals, Problem 8  (175.84 MB)
1 -From Geometry to Calculus, one more time  (116.28 MB)
10 -Continuous functions on compact intervals are uniformly continuous  (176.17 MB)
11 -Continuous functions on compact intervals are Riemann integrable  (61.46 MB)
12 -Monotone functions on compact intervals are Riemann integrable  (56.13 MB)
13 -Some properties of oscillations and oscillatory sums  (194.25 MB)
14 -Some properties of Riemann integrals  (178.12 MB)
15 -Monotonicity of integrals  (72.5 MB)
16 -Additivity of integration w r t  the interval  (179.94 MB)
17 -Integrability of piecewise continuous functions  (140.83 MB)
18 -Mean Value Theorem for integrals 1  (117.39 MB)
19 -Mean Value Theorem for integrals 2  (116.43 MB)
2 -The concept of area  (126.42 MB)
20 -Mean value of a continuous function over a compact interval  (57.08 MB)
3 -Our early example  (56.78 MB)
4 -Integrability  (170.83 MB)
5 -Refinements of partitions, and relations between upper and lower Riemann sums  (235.75 MB)
6 -Integrable functions, an example  (64.37 MB)
7 -Finally, an example of a function that is not integrable  (59.68 MB)
8 -More practical tests for integrability (Cauchy, sequential)  (210.8 MB)
9 -Application of the new test to the example from V191  (67.3 MB)
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