Calculus 1 - mathandbolt

About Course

Embark on a comprehensive journey into the fundamentals of Calculus, Integration, and Elementary Differential Equations in this engaging first-year undergraduate course. Designed to equip students with a solid mathematical foundation, the curriculum covers essential topics such as limits, continuity, derivatives, integration, and basic differential equations.

Course Highlights:

Calculus Fundamentals: Master the core concepts of limits, continuity, and derivatives to develop a robust understanding of the building blocks of calculus.
Integration Techniques: Explore various methods of integration, including definite and indefinite integrals, substitution, and integration by parts, enabling you to analyze functions and calculate areas under curves.
Differential Equations: Introduce yourself to elementary differential equations and learn to solve first-order equations, providing a practical application of calculus concepts.
Real-World Applications: Apply mathematical principles to real-world scenarios, emphasizing problem-solving skills and critical thinking in areas such as optimization and related rates.
Interactive Learning: Engage in hands-on activities, problem-solving sessions, and collaborative projects to reinforce theoretical concepts and enhance your mathematical intuition.

Topics Include:

Limits
Power & Product Rule
Implicit Differentiation
First & Second Derivative Test
L’Hopital’s Rule
Integrals
Riemann Sums
Area Between Curves
Volume Method of Cylindrical Shells

Ready to unveil the magic of Calculus 1 and amplify your mathematical prowess? Enroll now and take the first stride toward mastering this indispensable mathematical skill!

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Limits & Continuity: Solve diverse limit problems and recognize function discontinuities.
Derivatives: Master key derivative rules, including the chain rule and implicit differentiation techniques.
Applications: Apply derivatives in real-world scenarios, tackling optimization and related rates in Calculus 1.
Covering integrals, the Fundamental Theorem of Calculus, and various integration techniques.
Exploring applications like volume of revolution using disks, washers, shells, and real-world scenarios.
Delving into Polar & Parametric, including sketching polar curves and determining bounded areas.

Course Content

1. Functions

1.1 Defining Functions

13:00
1.2 Even vs Odd Functions

13:42
1.3 Increasing and Decreasing Functions

04:02
1.4 Types of Functions

19:51
1.5 Composition of functions

15:58

2. Rate Of Change

3. Limits

4. Continuity

5. Intermediate Value Theorem

6. Derivative

6.1 Derivative From The Definition Of Limit

13:01
6.2 The Product Rule

00:00
6.3 The Quotient Rule

12:05
6.4 Rate Of Change

00:00
6.5 Trigonometric Differentiation

11:36
6.6 The Chain Rule

13:48
6.7 Inverse Trigonometric Differentiation

10:47
6.8 Equation Of The Tangent Line

13:12
6.9 Implicit Differentiation

17:57
6.10 Exponential And Logarithmic Differentiation

10:08
6.11 Derivative Of Hyperbolic And Inverse Hyperbolic Functions

39:30
6.12 Higher Order Derivatives

13:52

7. Application of Derivative

7.1 Related Rates

20:24
7.2 Linear Approximations

16:21
7.3 Absolute Maximum And Minimum

22:41
7.4 The Mean Value Theorem And Rolle’s theorem

17:40
7.5 Higher Order Derivative Test

32:23
7.6 Applied Optimizations

26:42
7.7 Newton’s Method

19:10
7.8 Curve Sketching

35:25
7.9 L’Hopital’s Rule

13:55

9. Integrals

10. Application Of Integrals

11. Snippets From Calculus II

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About Course

What Will You Learn?

Course Content

1. Functions

1.1 Defining Functions

1.2 Even vs Odd Functions

1.3 Increasing and Decreasing Functions

1.4 Types of Functions

1.5 Composition of functions

2. Rate Of Change

2.1 Average And Instantaneous Rate Of Change

3. Limits

3.1 Investigation Of Limits

3.2 Algebraic Evaluation of Limits

4. Continuity

4.1 Continuity of Functions

5. Intermediate Value Theorem

5.1 Intermediate Value Theorem

6. Derivative

6.1 Derivative From The Definition Of Limit

6.2 The Product Rule

6.3 The Quotient Rule

6.4 Rate Of Change

6.5 Trigonometric Differentiation

6.6 The Chain Rule

6.7 Inverse Trigonometric Differentiation

6.8 Equation Of The Tangent Line

6.9 Implicit Differentiation

6.10 Exponential And Logarithmic Differentiation

6.11 Derivative Of Hyperbolic And Inverse Hyperbolic Functions

6.12 Higher Order Derivatives

7. Application of Derivative

7.1 Related Rates

7.2 Linear Approximations

7.3 Absolute Maximum And Minimum

7.4 The Mean Value Theorem And Rolle’s theorem

7.5 Higher Order Derivative Test

7.6 Applied Optimizations

7.7 Newton’s Method

7.8 Curve Sketching

7.9 L’Hopital’s Rule

9. Integrals

9.1 Approximating Areas

9.2 Reimann Sum, Definite Integrals and The Fundamental Theorem Of Calculus

9.3 Integration By The Method Of Substitution

10. Application Of Integrals

10.1 Area Between Two Curves

10.2 Finding Volume by Method of Disks and Washers

10.2 Finding Volume by Method of Cylindrical Shells

10.3 Average Value Of A Function

11. Snippets From Calculus II

11.1 Graphing f, f’, f”

11.2 Slope Fields for Differential Equations

11.3 Differential Equations – Variable Separable Form

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