English | MP4 | AVC 1280×720 | AAC 44KHz 2ch | 18.5 Hours | 1.66 GB
Learn everything from Calculus 1, then test your knowledge with 600+ practice questions
HOW BECOME A CALCULUS 1 MASTER IS SET UP TO MAKE COMPLICATED MATH EASY:
This 395-lesson course includes video and text explanations of everything from Calculus 1, and it includes 110 quizzes (with solutions!) and an additional 28 workbooks with extra practice problems, to help you test your understanding along the way. Become a Calculus 1 Master is organized into the following sections:
Precalculus
Limits & Continuity
Derivatives
Applications of Derivatives
AND HERE’S WHAT YOU GET INSIDE OF EVERY SECTION:
Videos: Watch over my shoulder as I solve problems for every single math issue you’ll encounter in class. We start from the beginning… I explain the problem setup and why I set it up that way, the steps I take and why I take them, how to work through the yucky, fuzzy middle parts, and how to simplify the answer when you get it.
Notes: The notes section of each lesson is where you find the most important things to remember. It’s like Cliff Notes for books, but for math. Everything you need to know to pass your class and nothing you don’t.
Quizzes: When you think you’ve got a good grasp on a topic within a course, you can test your knowledge by taking one of the quizzes. If you pass, great! If not, you can review the videos and notes again or ask for help in the Q&A section.
Workbooks: Want even more practice? When you’ve finished the section, you can review everything you’ve learned by working through the bonus workbook. The workbooks include tons of extra practice problems, so they’re a great way to solidify what you just learned in that section.
What you’ll learn
- Precalculus, including functions, their graphs, and how to modify functions
- Limits & Continuity, including how to solve every kind of limit problem, and how to find discontinuities in a function
- Derivatives, including all of the derivative rules, the infamous chain rule, and how to do implicit differentiation
- Applications of Derivatives, including two of the hardest topics from Calc 1: optimization and related rates
Table of Contents
Calculus 1 – Introduction & Resources
1 Hi! START HERE: Course overview
2 Download the Calc 1 formula sheet
Foundations of Calculus – Functions
3 Introduction to functions
4 RESOURCE: Quiz solutions for this section
5 Introduction to functions
6 Vertical line test
7 Vertical line test
8 Domain and range
9 Domain and range from a graph
10 Domain and range from a graph
11 Even, odd, or neither
12 Independent and dependent variables
13 BONUS! Extra practice problems.
Foundations of Calculus – Graphing functions
14 Introduction to graphing functions
15 RESOURCE: Quiz solutions for this section
16 Equation modeling
17 Modeling a piecewise-defined function
18 Sketching graphs from story problems
19 Equation of a line in point-slope form
20 Equation of a line in point-slope form
21 Equation of a line in slope-intercept form
22 Equation of a line in slope-intercept form
23 Graphing parabolas
24 Finding center and radius of a circle
25 Graphing circles
26 BONUS! Extra practice problems.
Foundations of Calculus – Modifying functions
27 Introduction to modifying functions
28 RESOURCE: Quiz solutions for this section
29 Combinations of functions
30 Composite functions
31 Composite functions, domain
32 BONUS! Extra practice problems.
Foundations of Calculus – Inverse functions and logarithms
33 Introduction to inverse functions and logarithms
34 RESOURCE: Quiz solutions for this section
35 Horizontal line test (1-to-1)
36 Horizontal line test (1-to-1)
37 Inverse functions
38 Finding the equation of a function from points on its inverse
39 Laws of logarithms
40 BONUS! Extra practice problems.
Foundations of Calculus – Other functions and trigonometry
41 Introduction to other functions and trigonometry
42 RESOURCE: Quiz solutions for this section
43 Quadratic formula
44 Quadratic formula
45 Completing the square
46 Completing the square
47 Long division of polynomials
48 Long division of polynomials
49 Unit circle
50 BONUS! Extra practice problems.
Limits & Continuity – Idea of the limit
51 Introduction to idea of the limit
52 RESOURCE: Quiz solutions for this section
53 Introduction to limits and continuity
54 Idea of the limit
55 BONUS! Extra practice problems.
Limits & Continuity – Formal definition of the limit
56 Introduction to formal definition of the limit
57 RESOURCE: Quiz solutions for this section
58 One-sided limits
59 One-sided limits
60 Proving that the limit does not exist
61 Precise definition of the limit
62 Precise definition of the limit
63 Precise definition of the limit, finding delta
64 BONUS! Extra practice problems.
Limits & Continuity – Combinations and composites
65 Introduction to combinations and composites
66 RESOURCE: Quiz solutions for this section
67 Limits of combinations
68 Limits of composites
69 BONUS! Extra practice problems.
Limits & Continuity – Continuity
70 Introduction to continuity
71 RESOURCE: Quiz solutions for this section
72 Introduction to continuity
73 Introduction to continuity
74 Removable discontinuities
75 Jump discontinuities
76 Infinite/essential discontinuities
77 BONUS! Extra practice problems.
Limits & Continuity – Intermediate value theorem
78 Introduction to intermediate value theorem
79 RESOURCE: Quiz solutions for this section
80 Intermediate value theorem
81 Intermediate value theorem
82 Intermediate value theorem with an interval
83 Intermediate value theorem without an interval
84 BONUS! Extra practice problems.
Limits & Continuity – Solving limits
85 Introduction to solving limits
86 RESOURCE: Quiz solutions for this section
87 Solving with substitution
88 Solving with substitution
89 Solving with factoring
90 Solving with factoring
91 Solving with conjugate method
92 Solving with conjugate method
93 Infinite limits (vertical asymptotes)
94 Infinite limits (vertical asymptotes)
95 Crazy graphs
96 Trigonometric limits
97 Trigonometric limits
98 Making the function continuous
99 Making the function continuous
100 BONUS! Extra practice problems.
Limits & Continuity – Squeeze theorem
101 Introduction to squeeze theorem
102 RESOURCE: Quiz solutions for this section
103 Squeeze theorem
104 Squeeze theorem
105 Squeeze theorem, limit of an inequality
106 BONUS! Extra practice problems.
Derivatives – Definition of the derivative
107 Introduction to definition of the derivative
108 RESOURCE: Quiz solutions for this section
109 Introduction to derivatives
110 Difference quotient
111 Definition of the derivative
112 Definition of the derivative
113 BONUS! Extra practice problems.
Derivatives – Derivative rules
114 Introduction to derivative rules
115 RESOURCE: Quiz solutions for this section
116 Power rule
117 Power rule
118 Power rule, example 2
119 Power rule for negative exponents or powers in the denominator
120 Power rule for fractional powers or radicals
121 Product rule, two functions
122 Product rule, two functions
123 Product rule, three or more functions
124 Product rule, three or more functions
125 Quotient rule
126 Quotient rule
127 Reciprocal rule
128 Reciprocal rule
129 BONUS! Extra practice problems.
Derivatives – Chain rule
130 Introduction to chain rule
131 RESOURCE: Quiz solutions for this section
132 Chain rule with power rule
133 Chain rule with power rule
134 Chain rule with product rule
135 Chain rule with product rule
136 Chain rule with quotient rule
137 Chain rule with quotient rule
138 Chain rule with trig functions
139 Chain rule with trig functions
140 BONUS! Extra practice problems.
Derivatives – Derivatives of trig functions
141 Introduction to derivatives of trig functions
142 RESOURCE: Quiz solutions for this section
143 Trigonometric derivatives
144 Trigonometric derivatives
145 Trigonometric derivatives, cotangent
146 Inverse trigonometric derivatives
147 Inverse trigonometric derivatives, arcsine
148 Inverse trigonometric derivatives, arccotangent
149 Hyperbolic derivatives
150 Hyperbolic derivatives
151 Inverse hyperbolic derivatives
152 Inverse hyperbolic derivatives
153 BONUS! Extra practice problems.
Derivatives – Derivatives of ln(x) and e^x
154 Introduction to derivatives of ln(x) and e^x
155 RESOURCE: Quiz solutions for this section
156 Exponential derivatives
157 Exponential derivatives
158 Logarithmic derivatives
159 Logarithmic derivatives
160 Logarithmic derivatives, example 2
161 Logarithmic differentiation
162 Logarithmic differentiation, example 2
163 Derivative of x^x
164 BONUS! Extra practice problems.
Derivatives – Tangent and normal lines
165 Introduction to tangent and normal lines
166 RESOURCE: Quiz solutions for this section
167 Tangent lines
168 Tangent lines
169 Value that makes two tangent lines parallel
170 Values that make the function differentiable
171 Horizontal and vertical tangent lines and differentiability
172 Horizontal and vertical tangent lines and differentiability
173 Normal lines
174 Normal lines
175 Average rate of change
176 Average rate of change
177 BONUS! Extra practice problems.
Derivatives – Implicit differentiation
178 Introduction to implicit differentiation
179 RESOURCE: Quiz solutions for this section
180 Implicit differentiation
181 Implicit differentiation
182 Equation of the tangent line
183 Equation of the tangent line
184 Equation of the tangent line, example 2
185 Second derivatives
186 Second derivatives
187 BONUS! Extra practice problems.
Applications of Derivatives – Optimization
188 Introduction to optimization
189 RESOURCE: Quiz solutions for this section
190 Optimization
191 Optimization
192 Critical points
193 Increasing and decreasing
194 First derivative test
195 Concavity
196 Second derivative test
197 BONUS! Extra practice problems.
Applications of Derivatives – Sketching graphs
198 Introduction to sketching graphs
199 RESOURCE: Quiz solutions for this section
200 Vertical asymptotes
201 Horizontal asymptotes
202 Slant asymptotes
203 Sketching graphs
204 Extrema on a closed interval
205 Extrema on a closed interval
206 Sketching f(x) given f'(x), or vice versa
207 BONUS! Extra practice problems.
Applications of Derivatives – Linear approximation
208 Introduction to linear approximation
209 RESOURCE: Quiz solutions for this section
210 Linear approximation
211 Linear approximation
212 Linear approximation to estimate a root
213 Linearization
214 BONUS! Extra practice problems.
Applications of Derivatives – Related rates
215 Introduction to related rates
216 RESOURCE: Quiz solutions for this section
217 Introduction to related rates
218 Introduction to related rates
219 Radius of the balloon
220 Price of the product
221 Water level in the tank
222 Observer and the airplane
223 Ladder sliding down the wall
224 BONUS! Extra practice problems.
Applications of Derivatives – Applied optimization
225 Introduction to applied optimization
226 RESOURCE: Quiz solutions for this section
227 Applied optimization
228 Dimensions of a rectangle that maximize its area
229 Dimensions of a rectangle that minimize its perimeter
230 Dimensions that minimize page size with a given printed area
231 Two real numbers with minimum product
232 Two real numbers with minimum sum of squares
233 Point on the line closest to another point
234 Time when velocity is minimum
235 Dimensions that maximize the volume of a box
236 Dimensions that minimize the surface area of an open top box
237 Width that minimizes the surface area of an open top box
238 Dimensions that maximize the volume of a cylinder
239 Dimensions that minimize the surface area of a cylinder
240 Maximum volume of a cone-shaped cup
241 Production level and sale price that maximize profit
242 Sales level that maximizes revenue
243 Maximum area of a rectangle inscribed in a semicircle
244 Dimensions that maximize the area of a rectangle inscribed in a triangle
245 Maximum volume of a cylinder inscribed in a sphere
246 BONUS! Extra practice problems.
Applications of Derivatives – Derivative theorems
247 Introduction to derivative theorems
248 RESOURCE: Quiz solutions for this section
249 Mean value theorem
250 Mean value theorem
251 Rolle’s theorem
252 Rolle’s theorem
253 Newton’s method
254 Newton’s method
255 L’Hospital’s rule
256 L’Hospital’s rule
257 Limits at infinity (horizontal asymptotes)
258 Limits at infinity (horizontal asymptotes)
259 BONUS! Extra practice problems.
Applications of Derivatives – Physics
260 Introduction to physics
261 RESOURCE: Quiz solutions for this section
262 Position function
263 Position function
264 Position function of a particle
265 Vertical motion
266 Vertical motion, ball thrown up from the ground
267 Vertical motion, coin dropped from the roof
268 BONUS! Extra practice problems.
Applications of Derivatives – Economics
269 Introduction to economics
270 RESOURCE: Quiz solutions for this section
271 Marginal cost, revenue, and profit
272 Marginal cost, revenue, and profit
273 BONUS! Extra practice problems.
Applications of Derivatives – Exponential growth and decay
274 Introduction to exponential growth and decay
275 RESOURCE: Quiz solutions for this section
276 Half life
277 Half life
278 Compounding interest
279 Compounding interest
280 Sales decline
281 Sales decline
282 BONUS! Extra practice problems.
Final exam and wrap-up
283 Calculus 1 final exam
284 Wrap-up
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