single variable calculus learning repository with problem solvings
Handwritten notes (for real understanding) Problem-solving approach
it includes
- Intuition over memorization
- Mistakes and corrections
- Real thinking process
topics covered till now
-
Functions and Models
- Different types of Functions
- Vertical line Test
- linear Functions, Power Functions, Root Functions, Reciprocal Functions, Rational Functions, Algebric Functions, Exponential Functions, Inverse Log Functions
- Inverse Trigonometric Functions
- Rotation of axes
- Combinations of Functions
- Trig Identities
- Triangle formula
- Sigma Notations
-
Limits and Derivatives
- Rate of Change
- How a limit cant exist
- How a limit exists
- Limit Laws
- Continous Functions
- Methods to solve
- Squeeze Theorem
- Precise Definitions of limits
- Infinte Limits
- Limits at Infinity
- Infinte Limits at infinity
- Methods to solve them
- Continuity
- A function is continous at number a
- Discontinuity
- Continous at an interval
- Methods of Continous Functions
- Intermediate Value Theorem
- Definition of Derivitive
- Tangent line at a point on a curve
- Differentiability
- Higher Derivatives
-
Derivatives of Polynomial and Exponential Functions
- Constant Functions
- Power Rule
- The Reason Discontinuity exists
- Product and Quotient Rule
- Constant Multiple Rule
- Rate of Change
- Derivatives of Trig Functions
- Chain Rule
- The Proof of Eulers number
- Why Euler number is approx 2.71828
- Non Differentiability
- Implicit Differentiation
- Growth Functions
- Euler Number (e) as a limit
- Linear Approximations
- Quadratic Approximation
- Derivative of Inverse Trigonometric Functions
- Derivative of an Inverse
- Hyperbolic Functions
- Hyperbolic Identities
- Derivative of Hyperbolic Functions
- Derivative of Inverse Hyperbolic Functions
- Hyperbolic functions into Log Functions
- Maximum and Minimum
- Supremum or Least Upper Bound
- Infimum or Greatest Lower Bound
- Application of Differentiation
-
Integration
- Common Integrations
- Integral of Rate Change is Net Change
- Riemann Sums
- Mid-Point Approximation
- Integration Techniques
- Areas Between Curves
- Volumes of Solids of Revolution
- Surface Area of Revolution
- Indeterminate Forms
- Integration by Parts
- Trig Integrals
- Trig Substitution
- Improper Integrals
- Partial Fractions
- Comparison Test
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The repo is for
- Students learning calculus from scratch
- Engineering students (especially AI, Quant)
- Anyone who wants deep conceptual clarity
Why this repo is different
- not ai generated notes
- this shows real learning process
- this shouws focuses on thinking, not copying
My Future goals
- I will add more advanced problems
- I want to include applications in physics and engineering
- I want to Connect calculus with programming
calculus, single variable calculus, MIT 18.01, integration, derivatives, engineering mathematics, problem solving, handwritten notes, deep learning math, quantitative finance math