julia-numerical

Included with Lifetime

$97 forever

Execute numerical calculations and mathematical computations using Julia. Use this skill for matrix operations, linear algebra, numerical integration, optimization, statistics, and scientific computing tasks.

General

What this skill does


# Julia Numerical Calculation Skill

This skill enables you to execute numerical calculations using Julia, a high-performance programming language designed for numerical and scientific computing.

## When to Use

Use this skill when you need to:
- Perform matrix operations and linear algebra
- Solve differential equations
- Execute numerical integration or optimization
- Calculate statistical measures
- Handle large-scale numerical computations
- Work with complex mathematical operations

## Setup

Before using this skill, ensure Julia is installed on your system:

```bash
# On macOS (using Homebrew)
brew install julia

# On Linux (Ubuntu/Debian)
sudo apt-get install julia

# On Windows (using Chocolatey)
choco install julia

# Or download from https://julialang.org/downloads/
```

## Basic Examples

### Linear Algebra

```julia
using LinearAlgebra

# Create matrices
A = [1 2; 3 4]
B = [5 6; 7 8]

# Matrix multiplication
C = A * B

# Eigenvalues and eigenvectors
eigenvals, eigenvecs = eigen(A)

# Matrix inverse
A_inv = inv(A)
```

### Numerical Integration

```julia
using QuadGK

# Define a function
f(x) = sin(x) * exp(-x)

# Integrate from 0 to ∞
result, error = quadgk(f, 0, Inf)
```

### Optimization

```julia
using Optim

# Define objective function
f(x) = (x[1] - 2)^2 + (x[2] - 3)^2

# Minimize
result = optimize(f, [0.0, 0.0])
```

### Statistics

```julia
using Statistics

data = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]

# Statistical measures
mean_val = mean(data)
std_val = std(data)
var_val = var(data)
median_val = median(data)
```

## How to Use This Skill

When you ask me to perform a numerical calculation:
1. I'll identify the appropriate Julia packages needed
2. Write Julia code to solve the problem
3. Execute the code
4. Return results and explanations

## Common Julia Packages

- **LinearAlgebra**: Matrix operations and linear algebra
- **Statistics**: Statistical functions
- **QuadGK**: Numerical integration
- **Optim**: Optimization algorithms
- **DifferentialEquations**: Solving differential equations
- **Plots**: Visualization
- **Distributions**: Probability distributions
- **Random**: Random number generation

## Notes

- Julia is JIT-compiled, so first runs may include compilation time
- Use `.jl` files for organizing longer scripts
- Install packages with `using Pkg; Pkg.add("PackageName")`
- Results are returned as Julia objects that are converted to readable format

Files: 3

Size: 8.0 KB

Complexity: 14/100

Category: General

Source: https://github.com/kongdd/skills_for_your_ai_student/tree/main/skills/julia-numerical

Related in General

modeling-omnistudio-epc-catalog

Included

Salesforce Industries CME EPC product-modeling skill for Product2-based catalog creation. Use when creating EPC products, configuring product attributes, building offer bundles with Product Child Items, or reviewing EPC DataPack JSON metadata for product catalog changes. TRIGGER when: user creates or updates Product2 EPC records, AttributeAssignment payloads, AttributeMetadata/AttributeDefaultValues, Offer bundles, or ProductChildItem relationships. DO NOT TRIGGER when: designing OmniScripts/FlexCards/Integration Procedures (use building-omnistudio-omniscript, building-omnistudio-flexcard, or building-omnistudio-integration-procedure), implementing Apex business logic (use generating-apex), or troubleshooting deployment pipelines (use deploying-metadata).

Generalscripts

relationship-science-coach

Included

Use this skill for direct, practical adult relationship coaching: couples conflict, repair, trust, marriage, dating, flirting, attachment patterns, emotional connection, sex, desire differences, eroticism, kink negotiation, affection, love languages, breakups, and long-term passion. Draw on Gottman, EFT and Hold Me Tight, attachment science, modern sex research, Perel, Nagoski, Kerner, Schnarch, Love and Stosny, and flexible love-language tools. Be concrete and low-hedge. Redirect only for imminent danger, abuse, coercive control, minors, non-consent, self-harm, stalking, or medical/legal/psychiatric decisions.

Generalscripts

building-sf-integrations

Included

Salesforce integration architecture and runtime plumbing with 120-point scoring. Use this skill to set up Named Credentials, External Credentials, External Services, REST/SOAP callout patterns, Platform Events, and Change Data Capture. TRIGGER when: user sets up Named Credentials, External Services, REST/SOAP callouts, Platform Events, CDC, or touches .namedCredential-meta.xml files. DO NOT TRIGGER when: Connected App/OAuth config (use configuring-connected-apps), Apex-only logic (use generating-apex), or data import/export (use handling-sf-data).

Generalscripts

venue-templates

Included

Access comprehensive LaTeX templates, formatting requirements, and submission guidelines for major scientific publication venues (Nature, Science, PLOS, IEEE, ACM), academic conferences (NeurIPS, ICML, CVPR, CHI), research posters, and grant proposals (NSF, NIH, DOE, DARPA). This skill should be used when preparing manuscripts for journal submission, conference papers, research posters, or grant proposals and need venue-specific formatting requirements and templates.

Generalscripts

let-fate-decide

Included

Draws the 12 Houses of the Zodiac Tarot spread to inject entropy into planning when prompts are vague, ambiguous, or casually delegated. Interprets the spread to guide next steps. Use when the user says 'let fate decide', 'YOLO', 'whatever', 'idk', or other nonchalant phrases, makes Yu-Gi-Oh references, or when you are about to arbitrarily pick between multiple reasonable approaches. Prefer over ask-questions-if-underspecified when the user's tone is casual or playful rather than precision-seeking.

Generalscripts

net-ops

Included

Cross-platform network troubleshooting (Windows, macOS, Linux) via local or remote shell. Use for: DNS broken, can't resolve hostnames, nslookup/dig works but apps fail, NRPT, WFP, scutil, /etc/resolver, systemd-resolved, /etc/resolv.conf, NetworkManager, VPN DNS leak residue (ProtonVPN/Mullvad/WireGuard/AnyConnect), AV/firewall blocking DNS or DoH, Tailscale DNS interaction, intermittent connectivity, remote diagnostics over SSH.

Generalscripts