single variable calculus learning repository with problem solvings
Handwritten notes (for real understanding) Problem-solving approach
it includes
- Functions and Models
- Limits and Derivatives
- Derivatives of Polynomial and Exponential Functions
- Integration
- Application of Integration
topics covered till now
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root((Functions and Models))
Function Types
Function Types
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Linear Functions
Power Functions
Root Functions
Reciprocal Functions
Rational Functions
Algebraic Functions
Exponential Functions
Logarithmic Functions
Inverse Trigonometric Functions
Function Analysis
Vertical Line Test
Domain and Range
Combinations of Functions
Transformations
Rotation of Axes
Shifts and Scaling
Trigonometric Foundations
Trig Identities
Triangle Formula
Inverse Trig Functions
Notation
Sigma Notation
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root((Limits and Derivatives))
Limits
Core Concepts
Rate of Change
How a Limit Exists
How a Limit Cannot Exist
Precise Definition of Limits
Limit Laws
Solving Limits
Methods to Solve
Squeeze Theorem
Infinite Limits
Infinite Limits
Limits at Infinity
Infinite Limits at Infinity
Methods to Solve Them
Continuity
Definition
A Function is Continuous at Number a
Types
Discontinuity
Continuous on an Interval
Theorems
Methods of Continuous Functions
Intermediate Value Theorem
Derivatives
Definition of Derivative
Tangent Line at a Point on a Curve
Differentiability
Higher Derivatives
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root((Derivatives))
Basic Derivative Rules
Constant Functions
Power Rule
Constant Multiple Rule
The Reason Discontinuity Exists
Rate of Change
Advanced Rules
Product and Quotient Rule
Chain Rule
Implicit Differentiation
Exponential and Logarithmic
Euler Number e
Proof of Euler's Number
Why e ≈ 2.71828
Euler Number as a Limit
Growth Functions
Hyperbolic Functions
Hyperbolic Identities
Derivative of Hyperbolic Functions
Derivative of Inverse Hyperbolic Functions
Hyperbolic Functions into Log Functions
Trigonometric Derivatives
Derivatives of Trig Functions
Derivative of Inverse Trigonometric Functions
Derivative of an Inverse
Approximations
Linear Approximations
Quadratic Approximation
Non-Differentiability
Extrema and Bounds
Maximum and Minimum
Supremum or Least Upper Bound
Infimum or Greatest Lower Bound
Applications
Application of Differentiation
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root((Integration))
Core Concepts
Common Integrations
Integral of Rate of Change is Net Change
Riemann Sums
Mid-Point Approximation
Integration Techniques
Integration by Parts
Trig Integrals
Trig Substitution
Partial Fractions
Applications
Areas Between Curves
Volumes of Solids of Revolution
Surface Area of Revolution
Improper Integrals
Comparison Test
Indeterminate Forms
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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