Overview

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Embark on a comprehensive journey through Calculus 1 with this extensive 5-hour 22-minute video course. Master fundamental concepts including limits, continuity, derivatives, integrals, and their applications. Explore topics such as the Intermediate Value Theorem, Rolle's Theorem, and the Mean Value Theorem. Learn essential techniques like implicit differentiation, related rates, and u-substitution for integration. Dive deep into the theory behind calculus, including the construction of definite integrals via Riemann sums and the Fundamental Theorem of Calculus. Practice with numerous examples covering various aspects of calculus, from basic limit calculations to complex integration problems. Gain a solid foundation in calculus that prepares you for advanced mathematical studies and real-world applications in science and engineering.

Syllabus

2) Computing Limits from a Graph .
3) Computing Basic Limits by plugging in numbers and factoring .
4) Limit using the Difference of Cubes Formula 1 .
5) Limit with Absolute Value .
6) Limit by Rationalizing .
7) Limit of a Piecewise Function .
8) Trig Function Limit Example 1 .
9) Trig Function Limit Example 2 .
10) Trig Function Limit Example 3 .
11) Continuity .
12) Removable and Nonremovable Discontinuities .
13) Intermediate Value Theorem .
14) Infinite Limits .
15) Vertical Asymptotes .
16) Derivative (Full Derivation and Explanation) .
17) Definition of the Derivative Example .
18) Derivative Formulas .
19) More Derivative Formulas .
20) Product Rule .
21) Quotient Rule .
22) Chain Rule .
23) Average and Instantaneous Rate of Change (Full Derivation) .
24) Average and Instantaneous Rate of Change (Example) .
25) Position, Velocity, Acceleration, and Speed (Full Derivation) .
26) Position, Velocity, Acceleration, and Speed (Example) .
27) Implicit versus Explicit Differentiation .
28) Related Rates .
29) Critical Numbers .
30) Extreme Value Theorem .
31) Rolle's Theorem .
32) The Mean Value Theorem .
33) Increasing and Decreasing Functions using the First Derivative .
34) The First Derivative Test .
35) Concavity, Inflection Points, and the Second Derivative .
36) The Second Derivative Test for Relative Extrema .
37) Limits at Infinity .
38) Newton's Method .
39) Differentials: Deltay and dy .
40) Indefinite Integration (theory) .
41) Indefinite Integration (formulas) .
41) Integral Example .
42) Integral with u substitution Example 1 .
43) Integral with u substitution Example 2 .
44) Integral with u substitution Example 3 .
45) Summation Formulas .
46) Definite Integral (Complete Construction via Riemann Sums) .
47) Definite Integral using Limit Definition Example .
48) Fundamental Theorem of Calculus .
49) Definite Integral with u substitution .
50) Mean Value Theorem for Integrals and Average Value of a Function .
51) Extended Fundamental Theorem of Calculus (Better than 2nd FTC) .
error here: forgot to cube the (3/2) here at the end, otherwise ok!.
53) The Natural Logarithm ln(x) Definition and Derivative .
54) Integral formulas for 1/x, tan(x), cot(x), csc(x), sec(x), csc(x) .
55) Derivative of e^x and it's Proof .
56) Derivatives and Integrals for Bases other than e .
57) Integration Example 1 .
58) Integration Example 2 .
59) Derivative Example 1 .
60) Derivative Example 2 .