Module IV — Scientific Computing in Python

Unit 18 · 2 hrs

NumPy Arrays

Numerical Python — foundation of scientific computing

Why NumPy? Python lists are slow for math. NumPy arrays are stored as contiguous memory blocks (C-style), enabling vectorized operations that are 10–100× faster.

Creating Arrays

import numpy as np

np.array([1,2,3])           # from list → 1D array
np.array([[1,2],[3,4]])     # 2D array (matrix)
np.zeros((3,4))              # 3×4 zeros
np.ones((2,3))               # 2×3 ones
np.arange(0, 10, 2)          # [0,2,4,6,8]
np.linspace(0, 1, 5)         # 5 evenly spaced [0..1]
np.eye(3)                     # 3×3 identity matrix
np.random.rand(2,3)          # 2×3 random [0,1)

Array Attributes & Indexing

a = np.array([[1,2,3],[4,5,6]])
a.shape     # (2, 3)
a.ndim      # 2
a.dtype     # int64
a.size      # 6 (total elements)

a[0, 1]     # 2  (row 0, col 1)
a[1, :]     # [4,5,6]  (all of row 1)
a[:, 2]     # [3,6]    (all of col 2)
a[0:2, 1:3] # [[2,3],[5,6]]  (submatrix)

# Boolean indexing
a[a > 3]    # [4, 5, 6]

Array Operations

a = np.array([1,2,3])
b = np.array([4,5,6])

a + b        # [5, 7, 9]   element-wise
a * b        # [4, 10, 18] element-wise
a ** 2       # [1, 4, 9]
np.dot(a,b)  # 32  (dot product)
np.sum(a)    # 6
np.mean(a)   # 2.0
np.max(a)    # 3
a.reshape(3,1) # column vector

Unit 19 · 3 hrs

Universal Functions & Broadcasting

Universal Functions (ufuncs)

Ufuncs operate element-wise on arrays. They're implemented in C — much faster than Python loops.

# Math ufuncs
np.sqrt([4,9,16])   # [2., 3., 4.]
np.exp([1,2])        # [e, e²]
np.log([1,10,100])  # natural log
np.sin(np.pi/2)     # 1.0
np.abs([-1,-2,3])   # [1, 2, 3]

Broadcasting Rules

Broadcasting lets NumPy operate on arrays of different shapes without copying data.

Rule	Description
1	If arrays differ in ndim, pad smaller shape with 1s on LEFT
2	Dimensions of size 1 are stretched to match the other
3	Sizes must match or be 1 — otherwise ValueError

a = np.array([[1],[2],[3]])  # shape (3,1)
b = np.array([10,20,30])    # shape (3,)
a + b  # shape (3,3) — broadcasts both
# [[11,21,31],[12,22,32],[13,23,33]]

Fancy Indexing

a = np.array([10,20,30,40,50])
a[[0,2,4]]     # [10, 30, 50] — index with list
a[a > 25]      # [30, 40, 50] — boolean mask
a[a % 20 == 0] # [20, 40]

Unit 20 · 3 hrs

Pandas — Series & DataFrames

Pandas in simple words: Pandas helps you work with table-like data (like Excel sheets) in Python. If NumPy is for fast numbers, Pandas is for real-world data with row names, column names, missing values, filtering, and summaries.

Series vs DataFrame (for beginners)

Object	Think of it as	Shape	Example
Series	One labeled column	1D	Ages of students
DataFrame	Full table (many columns)	2D	Name + Age + Score table

Memory trick: Series = single lane. DataFrame = full highway with many lanes.

Series

A Series is one column of data with labels (index). You can access values by label or by position.

import pandas as pd

# From list (default int index)
s = pd.Series([10,20,30])

# From dict (keys become index)
s = pd.Series({'a':10, 'b':20})
s['a']     # 10
s.values   # numpy array
s.index    # Index(['a','b'])

DataFrame

A DataFrame is a 2D table made of multiple Series sharing the same row index.

df = pd.DataFrame({
    'Name': ['Alice','Bob','Carol'],
    'Age':  [25, 30, 22],
    'Score':[88, 72, 95]
})

df.head(2)          # first 2 rows
df.shape            # (3, 3)
df.dtypes           # column types
df['Age']           # Series (column)
df[['Name','Score']] # sub-DataFrame
df.iloc[0]          # first row by position
df.loc[0, 'Name']   # label-based: 'Alice'
df[df['Score'] > 80]# filter rows

Key DataFrame Operations

Operation	Code
Describe stats	`df.describe()`
Sort by column	`df.sort_values('Age')`
Group & aggregate	`df.groupby('Dept')['Score'].mean()`
Drop column	`df.drop('Age', axis=1)`
Handle missing	`df.fillna(0) / df.dropna()`
From CSV	`pd.read_csv('file.csv')`
To CSV	`df.to_csv('out.csv', index=False)`

iloc vs loc: iloc = integer position (0-based). loc = label-based (uses index labels). Mixing them up is a common bug.

Unit 21 · 2 hrs

Matplotlib — Basic Plotting

import matplotlib.pyplot as plt

# Simple example: heights of students (bar chart)
students = ['Asha', 'Ben', 'Chen', 'Diya', 'Evan']
heights = [152, 160, 155, 167, 162]

plt.bar(students, heights)
plt.title('Heights of Students in a Class')
plt.xlabel('Student')
plt.ylabel('Height (cm)')
plt.show()

Output of bar chart showing heights of students — Output: Student-height bar chart.

Chart Types

Chart	Function	Use For
Line plot	`plt.plot(x, y)`	Trends over continuous x
Scatter plot	`plt.scatter(x, y)`	Correlation between two vars
Bar chart	`plt.bar(categories, values)`	Comparing discrete categories
Histogram	`plt.hist(data, bins=10)`	Distribution of a variable
Pie chart	`plt.pie(sizes, labels=labels)`	Proportions of a whole

Output showing scatter, bar, histogram, and pie charts — Output: Examples of common chart types.

Subplots

# Compare two class sections side-by-side
students_a = ['Asha', 'Ben', 'Chen']
heights_a = [152, 160, 155]

students_b = ['Diya', 'Evan', 'Farah']
heights_b = [167, 162, 158]

fig, axes = plt.subplots(1, 2, figsize=(10,4))
axes[0].bar(students_a, heights_a); axes[0].set_title('Section A Heights')
axes[1].bar(students_b, heights_b); axes[1].set_title('Section B Heights')
plt.tight_layout()
plt.show()

Always call plt.show() last (in scripts). In Jupyter: use %matplotlib inline at the top.

Quick Review

Flashcards — Module IV

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