Calculus.mathlife -

| Week | Topic | Skill Goal | | :--- | :--- | :--- | | 1 | Limits & Continuity | Understand approaching a value, finding asymptotes | | 2 | Basic Derivatives (power, trig, exponential) | Compute derivative of any simple function | | 3 | Derivative rules (product, quotient, chain) | Handle composite functions | | 4 | Applications of derivatives (optimization, related rates) | Solve real-world max/min problems | | 5 | Antiderivatives & indefinite integrals | Reverse the derivative process | | 6 | Definite integrals & Riemann sums | Relate area to summation | | 7 | Fundamental Theorem of Calculus | Connect derivatives and integrals | | 8 | Basic integration techniques (u-substitution, parts) | Integrate more complex functions |

| Integral ( \int f(x) , dx ) | Result (plus constant ( C )) | | :--- | :--- | | ( \int x^n , dx ) (n ≠ -1) | ( \fracx^n+1n+1 ) | | ( \int \frac1x , dx ) | ( \ln |x| ) | | ( \int e^x , dx ) | ( e^x ) | | ( \int \cos x , dx ) | ( \sin x ) | | ( \int \sin x , dx ) | ( -\cos x ) | calculus.mathlife

Businesses use "marginal analysis" (a derivative concept) to find the exact point where producing one more unit of a product stops being profitable. | Week | Topic | Skill Goal |

Calculus is often treated as a wall of intimidating symbols and rigid rules. reimagines it as a dynamic toolkit for understanding change, motion, and the hidden patterns of the universe. It moves beyond the textbook to show how these mathematical concepts breathe life into everything from engineering to economics. Core Pillars It moves beyond the textbook to show how