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docs/1b/ece106.md

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 # ECE 106: Electricity and Magnetism
 
+## MATH 117 review
 
+!!! definition
+    A definite integral is composed of:
+    
+    - the **upper limit**, $b$,
+    - the **lower limit**, $a$,
+    - the **integrand**, $f(x)$, and
+    - the **differential element**, $dx$.
+
+$$\int^b_a f(x)\ dx$$
+
+The original function **cannot be recovered** from the result of a definite integral unless it is known that $f(x)$ is a constant.
+
+## N-dimensional integrals
+
+Much like how $dx$ represents an infinitely small line, $dx\cdot dy$ represents an infinitely small rectangle. This means that the surface area of an object can be expressed as:
+
+$$dS=dx\cdot dy$$
+
+Therefore, the area of a function can be expressed as:
+
+$$S=\int^x_0\int^y_0 dy\ dx$$
+
+where $y$ is usually equal to $f(x)$, changing on each iteration.
+
+!!! example
+    The area of a circle can be expressed as $y=\pm\sqrt{r^2-x^2}$. This can be reduced to $y=2\sqrt{r^2-x^2}$ because of the symmetry of the equation.
+    
+    $$
+    \begin{align*}
+    A&=\int^r_0\int^{\sqrt{r^2-x^2}}_0 dy\ dx \\
+    &=\int^r_0\sqrt{r^2-x^2}\ dx
+    \end{align*}
+    $$
+
+!!! warning
+    Similar to parentheses, the correct integral squiggly must be paired with the correct differential element.
+
+## Cartesian coordinates

docs/1b/ece108.md

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 # ECE 108: Discrete Math 1
 
+## Truth tables

docs/1b/ece140.md

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+# ECE 140: Linear Circuits
+
+## Voltage, current, and resistance

docs/1b/math119.md

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 # MATH 119: Calculus 2
+
+## Multivariable functions
+
+### Sketching multivariable functions